LMFDB - Embedded newform 175.2.x.a.12.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,2,Mod(3,175)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("175.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(175, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([21, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			12.1
Character	$\chi$	$=$	175.12
Dual form			175.2.x.a.73.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.43914 - 0.936298i) q^{2} +(2.98133 - 0.156245i) q^{3} +(3.58646 + 3.22926i) q^{4} +(-1.61949 - 1.54184i) q^{5} +(-7.41816 - 2.41031i) q^{6} +(-1.17017 - 2.37291i) q^{7} +(-3.35206 - 6.57879i) q^{8} +(5.88033 - 0.618047i) q^{9} +(2.50654 + 5.27708i) q^{10} +(0.0110705 - 0.105329i) q^{11} +(11.1969 + 9.06711i) q^{12} +(1.56081 + 0.247208i) q^{13} +(0.632446 + 6.88349i) q^{14} +(-5.06913 - 4.34368i) q^{15} +(1.00752 + 9.58587i) q^{16} +(2.51942 - 3.87956i) q^{17} +(-14.9216 - 3.99823i) q^{18} +(0.828774 + 0.920447i) q^{19} +(-0.829232 - 10.7595i) q^{20} +(-3.85940 - 6.89159i) q^{21} +(-0.125622 + 0.246547i) q^{22} +(0.0555245 - 0.144646i) q^{23} +(-11.0215 - 19.0898i) q^{24} +(0.245482 + 4.99397i) q^{25} +(-3.57557 - 2.06436i) q^{26} +(8.58862 - 1.36030i) q^{27} +(3.46600 - 12.2891i) q^{28} +(-4.84593 + 1.57454i) q^{29} +(8.29732 + 15.3411i) q^{30} +(0.611278 + 2.87584i) q^{31} +(2.69575 - 10.0607i) q^{32} +(0.0165478 - 0.315750i) q^{33} +(-9.77764 + 7.10387i) q^{34} +(-1.76357 + 5.64711i) q^{35} +(23.0854 + 16.7725i) q^{36} +(0.324588 - 0.400833i) q^{37} +(-1.15968 - 3.02108i) q^{38} +(4.69190 + 0.493139i) q^{39} +(-4.71479 + 15.8226i) q^{40} +(2.31834 + 3.19093i) q^{41} +(2.96104 + 20.4231i) q^{42} +(4.39882 - 4.39882i) q^{43} +(0.379839 - 0.342008i) q^{44} +(-10.4760 - 8.06558i) q^{45} +(-0.270864 + 0.300825i) q^{46} +(-4.24074 + 2.75397i) q^{47} +(4.50147 + 28.4212i) q^{48} +(-4.26142 + 5.55340i) q^{49} +(4.07708 - 12.4108i) q^{50} +(6.90505 - 11.9599i) q^{51} +(4.79947 + 5.92685i) q^{52} +(0.663649 + 12.6632i) q^{53} +(-22.2225 - 4.72354i) q^{54} +(-0.180329 + 0.153510i) q^{55} +(-11.6884 + 15.6524i) q^{56} +(2.61466 + 2.61466i) q^{57} +(13.2941 + 0.696716i) q^{58} +(11.3795 + 5.06647i) q^{59} +(-4.15332 - 31.9479i) q^{60} +(-3.48040 - 7.81711i) q^{61} +(1.20165 - 7.58691i) q^{62} +(-8.34753 - 13.2303i) q^{63} +(-4.66418 + 6.41969i) q^{64} +(-2.14656 - 2.80686i) q^{65} +(-0.335998 + 0.754665i) q^{66} +(-1.78216 - 1.15735i) q^{67} +(21.5639 - 5.77803i) q^{68} +(0.142937 - 0.439913i) q^{69} +(9.58897 - 12.1228i) q^{70} +(2.43082 + 7.48129i) q^{71} +(-23.7772 - 36.6137i) q^{72} +(-10.6211 + 8.60076i) q^{73} +(-1.16701 + 0.673776i) q^{74} +(1.51214 + 14.8503i) q^{75} +5.97747i q^{76} +(-0.262891 + 0.0969831i) q^{77} +(-10.9825 - 5.59585i) q^{78} +(-1.28595 + 6.04991i) q^{79} +(13.1482 - 17.0776i) q^{80} +(8.04241 - 1.70947i) q^{81} +(-2.66710 - 9.95377i) q^{82} +(-7.96975 + 4.06079i) q^{83} +(8.41316 - 37.1794i) q^{84} +(-10.0618 + 2.39838i) q^{85} +(-14.8479 + 6.61073i) q^{86} +(-14.2013 + 5.45136i) q^{87} +(-0.730047 + 0.280239i) q^{88} +(12.4217 - 5.53052i) q^{89} +(18.0007 + 29.4818i) q^{90} +(-1.23980 - 3.99294i) q^{91} +(0.666237 - 0.339465i) q^{92} +(2.27175 + 8.47830i) q^{93} +(12.9223 - 2.74672i) q^{94} +(0.0769888 - 2.76849i) q^{95} +(6.46499 - 30.4154i) q^{96} +(9.63928 + 4.91146i) q^{97} +(15.5938 - 9.55556i) q^{98} -0.626212i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{20}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.43914	−	0.936298i	−1.72473	−	0.662062i	−0.725085	−	0.688659i	$-0.758200\pi$
$2$	−2.43914	−	0.936298i	−1.72473	−	0.662062i	−0.999646	+	0.0265966i	$0.991533\pi$
$3$	2.98133	−	0.156245i	1.72127	−	0.0902079i	0.834089	−	0.551630i	$-0.185994\pi$
$3$	2.98133	−	0.156245i	1.72127	−	0.0902079i	0.887181	+	0.461422i	$0.152661\pi$
$4$	3.58646	+	3.22926i	1.79323	+	1.61463i
$5$	−1.61949	−	1.54184i	−0.724257	−	0.689530i
$5$	−1.61949	−	1.54184i	−0.724257	−	0.689530i
$6$	−7.41816	−	2.41031i	−3.02845	−	0.984003i
$7$	−1.17017	−	2.37291i	−0.442281	−	0.896876i
$7$	−1.17017	−	2.37291i	−0.442281	−	0.896876i
$8$	−3.35206	−	6.57879i	−1.18513	−	2.32595i
$9$	5.88033	−	0.618047i	1.96011	−	0.206016i
$10$	2.50654	+	5.27708i	0.792637	+	1.66876i
$11$	0.0110705	−	0.105329i	0.00333789	−	0.0317579i	−0.992726	−	0.120394i	$-0.961584\pi$
$11$	0.0110705	−	0.105329i	0.00333789	−	0.0317579i	0.996064	+	0.0886362i	$0.0282508\pi$
$12$	11.1969	+	9.06711i	3.23228	+	2.61745i
$13$	1.56081	+	0.247208i	0.432890	+	0.0685631i	0.369077	−	0.929399i	$-0.379674\pi$
$13$	1.56081	+	0.247208i	0.432890	+	0.0685631i	0.0638133	+	0.997962i	$0.479674\pi$
$14$	0.632446	+	6.88349i	0.169028	+	1.83969i
$15$	−5.06913	−	4.34368i	−1.30884	−	1.12153i
$16$	1.00752	+	9.58587i	0.251879	+	2.39647i
$17$	2.51942	−	3.87956i	0.611049	−	0.940933i	−0.388759	−	0.921339i	$-0.627096\pi$
$17$	2.51942	−	3.87956i	0.611049	−	0.940933i	0.999808	−	0.0195932i	$-0.00623712\pi$
$18$	−14.9216	−	3.99823i	−3.51706	−	0.942393i
$19$	0.828774	+	0.920447i	0.190134	+	0.211165i	0.830673	−	0.556760i	$-0.187956\pi$
$19$	0.828774	+	0.920447i	0.190134	+	0.211165i	−0.640539	+	0.767925i	$0.721289\pi$
$20$	−0.829232	−	10.7595i	−0.185422	−	2.40589i
$21$	−3.85940	−	6.89159i	−0.842191	−	1.50387i
$22$	−0.125622	+	0.246547i	−0.0267827	+	0.0525640i
$23$	0.0555245	−	0.144646i	0.0115777	−	0.0301609i	−0.927670	−	0.373402i	$-0.878191\pi$
$23$	0.0555245	−	0.144646i	0.0115777	−	0.0301609i	0.939247	+	0.343241i	$0.111525\pi$
$24$	−11.0215	−	19.0898i	−2.24975	−	3.89668i
$25$	0.245482	+	4.99397i	0.0490964	+	0.998794i
$26$	−3.57557	−	2.06436i	−0.701227	−	0.404853i
$27$	8.58862	−	1.36030i	1.65288	−	0.261791i
$28$	3.46600	−	12.2891i	0.655012	−	2.32242i
$29$	−4.84593	+	1.57454i	−0.899866	+	0.292384i	−0.722182	−	0.691703i	$-0.756861\pi$
$29$	−4.84593	+	1.57454i	−0.899866	+	0.292384i	−0.177684	+	0.984088i	$0.556861\pi$
$30$	8.29732	+	15.3411i	1.51488	+	2.80088i
$31$	0.611278	+	2.87584i	0.109789	+	0.516516i	0.998333	+	0.0577240i	$0.0183843\pi$
$31$	0.611278	+	2.87584i	0.109789	+	0.516516i	−0.888544	+	0.458792i	$0.848282\pi$
$32$	2.69575	−	10.0607i	0.476546	−	1.77850i
$33$	0.0165478	−	0.315750i	0.00288060	−	0.0549650i
$34$	−9.77764	+	7.10387i	−1.67685	+	1.21830i
$35$	−1.76357	+	5.64711i	−0.298098	+	0.954535i
$36$	23.0854	+	16.7725i	3.84756	+	2.79542i
$37$	0.324588	−	0.400833i	0.0533619	−	0.0658965i	−0.749766	−	0.661703i	$-0.769834\pi$
$37$	0.324588	−	0.400833i	0.0533619	−	0.0658965i	0.803128	+	0.595806i	$0.203167\pi$
$38$	−1.15968	−	3.02108i	−0.188125	−	0.490083i
$39$	4.69190	+	0.493139i	0.751306	+	0.0789654i
$40$	−4.71479	+	15.8226i	−0.745474	+	2.50177i
$41$	2.31834	+	3.19093i	0.362064	+	0.498339i	0.950722	−	0.310043i	$-0.100344\pi$
$41$	2.31834	+	3.19093i	0.362064	+	0.498339i	−0.588658	+	0.808382i	$0.700344\pi$
$42$	2.96104	+	20.4231i	0.456898	+	3.15135i
$43$	4.39882	−	4.39882i	0.670814	−	0.670814i	−0.287090	−	0.957904i	$-0.592688\pi$
$43$	4.39882	−	4.39882i	0.670814	−	0.670814i	0.957904	+	0.287090i	$0.0926879\pi$
$44$	0.379839	−	0.342008i	0.0572629	−	0.0515597i
$45$	−10.4760	−	8.06558i	−1.56168	−	1.20235i
$46$	−0.270864	+	0.300825i	−0.0399367	+	0.0443542i
$47$	−4.24074	+	2.75397i	−0.618576	+	0.401708i	−0.815538	−	0.578703i	$-0.803559\pi$
$47$	−4.24074	+	2.75397i	−0.618576	+	0.401708i	0.196962	+	0.980411i	$0.436892\pi$
$48$	4.50147	+	28.4212i	0.649732	+	4.10224i
$49$	−4.26142	+	5.55340i	−0.608775	+	0.793343i
$50$	4.07708	−	12.4108i	0.576586	−	1.75516i
$51$	6.90505	−	11.9599i	0.966900	−	1.67472i
$52$	4.79947	+	5.92685i	0.665567	+	0.821907i
$53$	0.663649	+	12.6632i	0.0911593	+	1.73942i	0.536358	+	0.843991i	$0.319800\pi$
$53$	0.663649	+	12.6632i	0.0911593	+	1.73942i	−0.445199	+	0.895432i	$0.646867\pi$
$54$	−22.2225	−	4.72354i	−3.02410	−	0.642792i
$55$	−0.180329	+	0.153510i	−0.0243155	+	0.0206993i
$56$	−11.6884	+	15.6524i	−1.56193	+	2.09164i
$57$	2.61466	+	2.61466i	0.346320	+	0.346320i
$58$	13.2941	+	0.696716i	1.74560	+	0.0914832i
$59$	11.3795	+	5.06647i	1.48148	+	0.659599i	0.978790	−	0.204866i	$-0.0656760\pi$
$59$	11.3795	+	5.06647i	1.48148	+	0.659599i	0.502693	+	0.864465i	$0.332343\pi$
$60$	−4.15332	−	31.9479i	−0.536192	−	4.12446i
$61$	−3.48040	−	7.81711i	−0.445620	−	1.00088i	−0.987091	−	0.160159i	$-0.948799\pi$
$61$	−3.48040	−	7.81711i	−0.445620	−	1.00088i	0.541472	−	0.840719i	$-0.317867\pi$
$62$	1.20165	−	7.58691i	0.152609	−	0.963538i
$63$	−8.34753	−	13.2303i	−1.05169	−	1.66686i
$64$	−4.66418	+	6.41969i	−0.583022	+	0.802461i
$65$	−2.14656	−	2.80686i	−0.266248	−	0.348148i
$66$	−0.335998	+	0.754665i	−0.0413585	+	0.0928928i
$67$	−1.78216	−	1.15735i	−0.217726	−	0.141393i	0.431168	−	0.902272i	$-0.358102\pi$
$67$	−1.78216	−	1.15735i	−0.217726	−	0.141393i	−0.648894	+	0.760879i	$0.724768\pi$
$68$	21.5639	−	5.77803i	2.61501	−	0.700689i
$69$	0.142937	−	0.439913i	0.0172075	−	0.0529594i
$70$	9.58897	−	12.1228i	1.14610	−	1.44896i
$71$	2.43082	+	7.48129i	0.288485	+	0.887866i	0.985332	+	0.170646i	$0.0545856\pi$
$71$	2.43082	+	7.48129i	0.288485	+	0.887866i	−0.696847	+	0.717220i	$0.745414\pi$
$72$	−23.7772	−	36.6137i	−2.80217	−	4.31496i
$73$	−10.6211	+	8.60076i	−1.24310	+	1.00664i	−0.243778	+	0.969831i	$0.578387\pi$
$73$	−10.6211	+	8.60076i	−1.24310	+	1.00664i	−0.999322	+	0.0368115i	$0.988280\pi$
$74$	−1.16701	+	0.673776i	−0.135663	+	0.0783249i
$75$	1.51214	+	14.8503i	0.174607	+	1.71476i
$76$			5.97747i			0.685663i
$77$	−0.262891	+	0.0969831i	−0.0299592	+	0.0110523i
$78$	−10.9825	−	5.59585i	−1.24352	−	0.633606i
$79$	−1.28595	+	6.04991i	−0.144680	+	0.680668i	0.844691	+	0.535255i	$0.179784\pi$
$79$	−1.28595	+	6.04991i	−0.144680	+	0.680668i	−0.989371	+	0.145413i	$0.953549\pi$
$80$	13.1482	−	17.0776i	1.47001	−	1.90934i
$81$	8.04241	−	1.70947i	0.893601	−	0.189941i
$82$	−2.66710	−	9.95377i	−0.294532	−	1.09921i
$83$	−7.96975	+	4.06079i	−0.874794	+	0.445730i	−0.832920	−	0.553393i	$-0.813333\pi$
$83$	−7.96975	+	4.06079i	−0.874794	+	0.445730i	−0.0418738	+	0.999123i	$0.513333\pi$
$84$	8.41316	−	37.1794i	0.917951	−	4.05660i
$85$	−10.0618	+	2.39838i	−1.09136	+	0.260140i
$86$	−14.8479	+	6.61073i	−1.60109	+	0.712853i
$87$	−14.2013	+	5.45136i	−1.52254	+	0.584447i
$88$	−0.730047	+	0.280239i	−0.0778232	+	0.0298735i
$89$	12.4217	−	5.53052i	1.31670	−	0.586234i	0.376363	−	0.926472i	$-0.377175\pi$
$89$	12.4217	−	5.53052i	1.31670	−	0.586234i	0.940339	+	0.340239i	$0.110508\pi$
$90$	18.0007	+	29.4818i	1.89745	+	3.10765i
$91$	−1.23980	−	3.99294i	−0.129967	−	0.418573i
$92$	0.666237	−	0.339465i	0.0694600	−	0.0353916i
$93$	2.27175	+	8.47830i	0.235570	+	0.879159i
$94$	12.9223	−	2.74672i	1.33283	−	0.283303i
$95$	0.0769888	−	2.76849i	0.00789889	−	0.284041i
$96$	6.46499	−	30.4154i	0.659830	−	3.10426i
$97$	9.63928	+	4.91146i	0.978721	+	0.498683i	0.868750	−	0.495252i	$-0.164924\pi$
$97$	9.63928	+	4.91146i	0.978721	+	0.498683i	0.109971	+	0.993935i	$0.464924\pi$
$98$	15.5938	−	9.55556i	1.57522	−	0.965257i
$99$		−	0.626212i		−	0.0629366i
$100$	−15.2464	+	18.7034i	−1.52464	+	1.87034i
$101$	8.01192	−	4.62568i	0.797216	−	0.460273i	−0.0452808	−	0.998974i	$-0.514418\pi$
$101$	8.01192	−	4.62568i	0.797216	−	0.460273i	0.842497	+	0.538701i	$0.181085\pi$
$102$	−28.0404	+	22.7067i	−2.77641	+	2.24829i
$103$	−3.63672	−	5.60006i	−0.358337	−	0.551790i	0.612823	−	0.790220i	$-0.290034\pi$
$103$	−3.63672	−	5.60006i	−0.358337	−	0.551790i	−0.971160	+	0.238430i	$0.923367\pi$
$104$	−3.60560	−	11.0969i	−0.353558	−	1.08814i
$105$	−4.37545	+	17.1114i	−0.427000	+	1.66990i
$106$	10.2378	−	31.5086i	0.994381	−	3.06039i
$107$	−12.3906	+	3.32004i	−1.19784	+	0.320960i	−0.801980	−	0.597350i	$-0.796220\pi$
$107$	−12.3906	+	3.32004i	−1.19784	+	0.320960i	−0.395860	+	0.918311i	$0.629553\pi$
$108$	35.1955	+	22.8562i	3.38669	+	2.19934i
$109$	4.57476	−	10.2751i	0.438183	−	0.984175i	−0.550594	−	0.834773i	$-0.685599\pi$
$109$	4.57476	−	10.2751i	0.438183	−	0.984175i	0.988777	−	0.149401i	$-0.0477346\pi$
$110$	0.583578	−	0.205591i	0.0556420	−	0.0196024i
$111$	0.905075	−	1.24573i	0.0859059	−	0.118239i
$112$	21.5675	−	13.6078i	2.03793	−	1.28582i
$113$	−0.610226	+	3.85282i	−0.0574053	+	0.362443i	0.942218	+	0.335000i	$0.108736\pi$
$113$	−0.610226	+	3.85282i	−0.0574053	+	0.362443i	−0.999623	+	0.0274425i	$0.991264\pi$
$114$	−3.92942	−	8.82562i	−0.368024	−	0.826595i
$115$	−0.312942	+	0.148643i	−0.0291820	+	0.0138611i
$116$	−22.4643	−	10.0017i	−2.08576	−	0.928639i
$117$	9.33085	+	0.489009i	0.862638	+	0.0452089i
$118$	−23.0124	−	23.0124i	−2.11846	−	2.11846i
$119$	−12.1540	−	1.43862i	−1.11416	−	0.131878i
$120$	−11.5841	+	47.9090i	−1.05748	+	4.37347i
$121$	10.7487	+	2.28470i	0.977150	+	0.207700i
$122$	1.17004	+	22.3257i	0.105930	+	2.02127i
$123$	7.41030	+	9.15096i	0.668164	+	0.825114i
$124$	−7.09450	+	12.2880i	−0.637105	+	1.10350i
$125$	7.30233	−	8.46617i	0.653140	−	0.757237i
$126$	7.97331	+	40.0863i	0.710319	+	3.57117i
$127$	−1.52389	−	9.62146i	−0.135223	−	0.853767i	−0.958285	−	0.285815i	$-0.907736\pi$
$127$	−1.52389	−	9.62146i	−0.135223	−	0.853767i	0.823062	−	0.567952i	$-0.192264\pi$
$128$	−0.0831775	+	0.0540161i	−0.00735192	+	0.00477439i
$129$	12.4270	−	13.8016i	1.09414	−	1.21516i
$130$	2.60769	+	8.85614i	0.228710	+	0.776735i
$131$	−6.11663	+	5.50744i	−0.534413	+	0.481187i	−0.891586	−	0.452851i	$-0.850407\pi$
$131$	−6.11663	+	5.50744i	−0.534413	+	0.481187i	0.357174	+	0.934038i	$0.383740\pi$
$132$	1.07899	−	1.07899i	0.0939137	−	0.0939137i
$133$	1.21434	−	3.04368i	0.105296	−	0.263921i
$134$	3.26332	+	4.49158i	0.281908	+	0.388013i
$135$	−16.0065	−	11.0393i	−1.37762	−	0.950108i
$136$	−33.9681	−	3.57019i	−2.91274	−	0.306141i
$137$	−4.72248	−	12.3025i	−0.403468	−	1.05107i	−0.973346	−	0.229341i	$-0.926343\pi$
$137$	−4.72248	−	12.3025i	−0.403468	−	1.05107i	0.569878	−	0.821729i	$-0.306991\pi$
$138$	−0.760532	+	0.939179i	−0.0647408	+	0.0799482i
$139$	3.54704	+	2.57708i	0.300856	+	0.218585i	0.727963	−	0.685616i	$-0.240467\pi$
$139$	3.54704	+	2.57708i	0.300856	+	0.218585i	−0.427107	+	0.904201i	$0.640467\pi$
$140$	−24.5609	+	14.5581i	−2.07578	+	1.23038i
$141$	−12.2128	+	8.87308i	−1.02850	+	0.747248i
$142$	1.07561	−	20.5239i	0.0902633	−	1.72233i
$143$	0.0433172	−	0.161662i	0.00362236	−	0.0135188i
$144$	11.8490	+	55.7454i	0.987420	+	4.64545i
$145$	10.2756	+	4.92168i	0.853342	+	0.408724i
$146$	33.9591	−	11.0340i	2.81047	−	0.913178i
$147$	−11.8370	+	17.2223i	−0.976299	+	1.42047i
$148$	2.45851	−	0.389390i	0.202089	−	0.0320077i
$149$	−1.49934	−	0.865642i	−0.122830	−	0.0709162i	0.437326	−	0.899303i	$-0.355926\pi$
$149$	−1.49934	−	0.865642i	−0.122830	−	0.0709162i	−0.560156	+	0.828387i	$0.689259\pi$
$150$	10.2160	−	37.6378i	0.834131	−	3.07311i
$151$	−2.72492	−	4.71971i	−0.221751	−	0.384084i	0.733589	−	0.679594i	$-0.237844\pi$
$151$	−2.72492	−	4.71971i	−0.221751	−	0.384084i	−0.955340	+	0.295510i	$0.904511\pi$
$152$	3.27732	−	8.53772i	0.265826	−	0.692500i
$153$	12.4173	−	24.3702i	1.00388	−	1.97022i
$154$	0.732033	+	0.00958890i	0.0589889	+	0.000772696i
$155$	3.44411	−	5.59988i	0.276638	−	0.449793i
$156$	15.2348	+	16.9200i	1.21976	+	1.35468i
$157$	7.38005	+	1.97748i	0.588992	+	0.157820i	0.540993	−	0.841027i	$-0.318049\pi$
$157$	7.38005	+	1.97748i	0.588992	+	0.157820i	0.0479996	+	0.998847i	$0.484715\pi$
$158$	8.80112	−	13.5525i	0.700180	−	1.07818i
$159$	3.95711	+	37.6494i	0.313819	+	2.98579i
$160$	−19.8777	+	12.1368i	−1.57147	+	0.959495i
$161$	−0.408206	+	0.0375055i	−0.0321711	+	0.00295584i
$162$	−21.2171	−	3.36046i	−1.66698	−	0.264023i
$163$	−15.9981	−	12.9550i	−1.25307	−	1.01471i	−0.998868	−	0.0475606i	$-0.984855\pi$
$163$	−15.9981	−	12.9550i	−1.25307	−	1.01471i	−0.254198	−	0.967152i	$-0.581811\pi$
$164$	−1.98969	+	18.9306i	−0.155369	+	1.47823i
$165$	−0.513634	+	0.485839i	−0.0399863	+	0.0378226i
$166$	23.2414	−	2.44277i	1.80389	−	0.189596i
$167$	3.69194	+	7.24584i	0.285691	+	0.560700i	0.988597	−	0.150582i	$-0.0481148\pi$
$167$	3.69194	+	7.24584i	0.285691	+	0.560700i	−0.702907	+	0.711282i	$0.748115\pi$
$168$	−32.4014	+	48.4912i	−2.49982	+	3.74118i
$169$	−9.98872	−	3.24553i	−0.768363	−	0.249656i
$170$	26.7878	+	3.57089i	2.05453	+	0.273875i
$171$	5.44234	+	4.90031i	0.416186	+	0.374736i
$172$	29.9811	−	1.57124i	2.28604	−	0.119806i
$173$	11.2307	+	4.31105i	0.853852	+	0.327763i	0.745627	−	0.666363i	$-0.232150\pi$
$173$	11.2307	+	4.31105i	0.853852	+	0.327763i	0.108225	+	0.994126i	$0.465483\pi$
$174$	39.7430			3.01291
$175$	11.5630	−	6.42628i	0.874080	−	0.485781i
$176$	1.02082			0.0769475
$177$	34.7176	+	13.3268i	2.60953	+	1.00171i
$178$	−35.4766	+	1.85925i	−2.65908	+	0.139357i
$179$	−12.2574	−	11.0366i	−0.916161	−	0.824915i	0.0688110	−	0.997630i	$-0.478079\pi$
$179$	−12.2574	−	11.0366i	−0.916161	−	0.824915i	−0.984972	+	0.172715i	$0.944746\pi$
$180$	−11.5260	−	62.7567i	−0.859099	−	4.67761i
$181$	−17.4861	−	5.68158i	−1.29973	−	0.422308i	−0.424244	−	0.905548i	$-0.639460\pi$
$181$	−17.4861	−	5.68158i	−1.29973	−	0.422308i	−0.875488	+	0.483240i	$0.839460\pi$
$182$	−0.714524	+	10.9001i	−0.0529641	+	0.807973i
$183$	−11.5976	−	22.7616i	−0.857319	−	1.68258i
$184$	−1.13772	+	0.119579i	−0.0838738	+	0.00881549i
$185$	−1.14368	+	0.148682i	−0.0840854	+	0.0109313i
$186$	2.39709	−	22.8068i	0.175763	−	1.67228i
$187$	−0.380740	−	0.308317i	−0.0278424	−	0.0225464i
$188$	−24.1025	−	3.81747i	−1.75786	−	0.278417i
$189$	−13.2780	−	18.7883i	−0.965832	−	1.36665i
$190$	−2.77991	+	6.68064i	−0.201676	+	0.484664i
$191$	−2.67834	−	25.4827i	−0.193798	−	1.84386i	−0.469884	−	0.882728i	$-0.655704\pi$
$191$	−2.67834	−	25.4827i	−0.193798	−	1.84386i	0.276086	−	0.961133i	$-0.410962\pi$
$192$	−12.9024	+	19.8679i	−0.931150	+	1.43385i
$193$	0.535514	+	0.143491i	0.0385472	+	0.0103287i	0.278041	−	0.960569i	$-0.410315\pi$
$193$	0.535514	+	0.143491i	0.0385472	+	0.0103287i	−0.239494	+	0.970898i	$0.576982\pi$
$194$	−18.9130	−	21.0050i	−1.35787	−	1.50807i
$195$	−6.83814	−	8.03278i	−0.489690	−	0.575239i
$196$	−33.2168	+	6.15580i	−2.37263	+	0.439700i
$197$	1.61473	−	3.16908i	0.115045	−	0.225788i	−0.826303	−	0.563226i	$-0.809560\pi$
$197$	1.61473	−	3.16908i	0.115045	−	0.225788i	0.941348	+	0.337438i	$0.109560\pi$
$198$	−0.586321	+	1.52742i	−0.0416680	+	0.108549i
$199$	−1.30189	−	2.25493i	−0.0922882	−	0.159848i	0.816185	−	0.577790i	$-0.196085\pi$
$199$	−1.30189	−	2.25493i	−0.0922882	−	0.159848i	−0.908474	+	0.417942i	$0.862751\pi$
$200$	32.0314	−	18.3551i	2.26496	−	1.29790i
$201$	−5.49404	−	3.17199i	−0.387520	−	0.223735i
$202$	−23.8732	+	3.78114i	−1.67971	+	0.266040i
$203$	9.40678	+	9.65649i	0.660226	+	0.677753i
$204$	63.3862	−	20.5954i	4.43792	−	1.44197i
$205$	1.16536	−	8.74217i	0.0813920	−	0.610580i
$206$	3.62714	+	17.0644i	0.252715	+	1.18893i
$207$	0.237104	−	0.884885i	0.0164799	−	0.0615038i
$208$	−0.797163	+	15.2108i	−0.0552733	+	1.05468i
$209$	0.106125	−	0.0771042i	0.00734081	−	0.00533341i
$210$	26.6937	−	37.6404i	1.84204	−	2.59743i
$211$	2.95158	+	2.14445i	0.203195	+	0.147630i	0.684729	−	0.728797i	$-0.259920\pi$
$211$	2.95158	+	2.14445i	0.203195	+	0.147630i	−0.481534	+	0.876427i	$0.659920\pi$
$212$	−38.5126	+	47.5590i	−2.64505	+	3.26637i
$213$	8.41598	+	21.9244i	0.576653	+	1.50223i
$214$	33.3308	+	3.50321i	2.27845	+	0.239475i
$215$	−13.9061	+	0.341575i	−0.948388	+	0.0232952i
$216$	−37.7387	−	51.9429i	−2.56779	−	3.53427i
$217$	6.10881	−	4.81572i	0.414693	−	0.326912i
$218$	−20.7790	+	20.7790i	−1.40733	+	1.40733i
$219$	−30.3210	+	27.3011i	−2.04890	+	1.84484i
$220$	−1.14247	−	0.0317708i	−0.0770250	−	0.00214199i
$221$	4.89139	−	5.43244i	0.329030	−	0.365425i
$222$	−3.37398	+	2.19109i	−0.226446	+	0.147056i
$223$	−0.124073	−	0.783365i	−0.00830853	−	0.0524580i	0.983186	−	0.182608i	$-0.0584540\pi$
$223$	−0.124073	−	0.783365i	−0.00830853	−	0.0524580i	−0.991494	+	0.130150i	$0.958454\pi$
$224$	−27.0276	+	5.37589i	−1.80586	+	0.359192i
$225$	4.53002	+	29.2145i	0.302002	+	1.94763i
$226$	5.09581	−	8.82620i	0.338968	−	0.587110i
$227$	−4.97653	−	6.14551i	−0.330304	−	0.407892i	0.584756	−	0.811209i	$-0.301190\pi$
$227$	−4.97653	−	6.14551i	−0.330304	−	0.407892i	−0.915060	+	0.403318i	$0.867857\pi$
$228$	0.933948	+	17.8208i	0.0618522	+	1.18021i
$229$	20.5352	+	4.36489i	1.35700	+	0.288440i	0.828261	−	0.560342i	$-0.189330\pi$
$229$	20.5352	+	4.36489i	1.35700	+	0.288440i	0.528743	+	0.848782i	$0.322664\pi$
$230$	0.902484	−	0.0695544i	0.0595080	−	0.00458628i
$231$	−0.768611	+	0.330214i	−0.0505709	+	0.0217265i
$232$	26.6024	+	26.6024i	1.74653	+	1.74653i
$233$	17.3123	+	0.907297i	1.13416	+	0.0594390i	0.610161	−	0.792277i	$-0.291105\pi$
$233$	17.3123	+	0.907297i	1.13416	+	0.0594390i	0.524003	+	0.851717i	$0.324438\pi$
$234$	−22.3014	−	9.92922i	−1.45789	−	0.649093i
$235$	11.1140	+	2.07851i	0.724998	+	0.135587i
$236$	24.4511	+	54.9180i	1.59163	+	3.57486i
$237$	−2.88856	+	18.2377i	−0.187632	+	1.18466i
$238$	28.2983	+	14.8888i	1.83431	+	0.965095i
$239$	−6.02822	+	8.29714i	−0.389933	+	0.536697i	−0.958182	−	0.286160i	$-0.907621\pi$
$239$	−6.02822	+	8.29714i	−0.389933	+	0.536697i	0.568249	+	0.822857i	$0.307621\pi$
$240$	36.5307	−	52.9683i	2.35805	−	3.41909i
$241$	−11.2231	+	25.2076i	−0.722947	+	1.62376i	0.0573496	+	0.998354i	$0.481735\pi$
$241$	−11.2231	+	25.2076i	−0.722947	+	1.62376i	−0.780296	+	0.625410i	$0.784932\pi$
$242$	−24.0783	−	15.6366i	−1.54781	−	1.00516i
$243$	−1.48819	+	0.398760i	−0.0954675	+	0.0255804i
$244$	12.7612	−	39.2748i	0.816950	−	2.51431i
$245$	15.4638	−	2.42325i	0.987943	−	0.154816i
$246$	−9.50673	−	29.2587i	−0.606127	−	1.86547i
$247$	1.06602	+	1.64152i	0.0678290	+	0.104447i
$248$	16.8705	−	13.6614i	1.07128	−	0.867503i
$249$	−23.1260	+	13.3518i	−1.46555	+	0.846134i
$250$	−25.7382	+	13.8130i	−1.62783	+	0.873611i
$251$			0.542621i			0.0342499i	0.999853	+	0.0171250i	$0.00545131\pi$
$251$			0.542621i			0.0342499i	−0.999853	+	0.0171250i	$0.994549\pi$
$252$	12.7860	−	74.4062i	0.805439	−	4.68715i
$253$	−0.0146208	−	0.00744966i	−0.000919201	−	0.000468356i
$254$	−5.29157	+	24.8949i	−0.332023	+	1.56205i
$255$	−29.6228	+	8.72245i	−1.85505	+	0.546221i
$256$	15.7770	−	3.35351i	0.986063	−	0.209594i
$257$	−4.45204	−	16.6152i	−0.277711	−	1.03643i	−0.954003	−	0.299797i	$-0.903081\pi$
$257$	−4.45204	−	16.6152i	−0.277711	−	1.03643i	0.676293	−	0.736633i	$-0.263586\pi$
$258$	−43.2337	+	22.0286i	−2.69161	+	1.37144i
$259$	−1.33096	−	0.301178i	−0.0827020	−	0.0187143i
$260$	1.36555	−	16.9985i	0.0846880	−	1.05420i
$261$	−27.5225	+	12.2538i	−1.70360	+	0.758492i
$262$	20.0759	−	7.70642i	1.24029	−	0.476104i
$263$	−18.8054	+	7.21872i	−1.15959	+	0.445126i	−0.860676	−	0.509154i	$-0.829958\pi$
$263$	−18.8054	+	7.21872i	−1.15959	+	0.445126i	−0.298916	+	0.954279i	$0.596625\pi$
$264$	−2.13272	+	0.949549i	−0.131260	+	0.0584407i
$265$	18.4498	−	21.5311i	1.13336	−	1.32265i
$266$	−5.81173	+	6.28699i	−0.356340	+	0.385480i
$267$	36.1692	−	18.4291i	2.21352	−	1.12784i
$268$	−2.65427	−	9.90586i	−0.162135	−	0.605097i
$269$	−2.42544	+	0.515544i	−0.147882	+	0.0314332i	−0.281258	−	0.959632i	$-0.590752\pi$
$269$	−2.42544	+	0.515544i	−0.147882	+	0.0314332i	0.133376	+	0.991066i	$0.457418\pi$
$270$	28.7061	+	41.9132i	1.74700	+	2.55075i
$271$	−1.71463	+	8.06671i	−0.104157	+	0.490018i	0.894887	+	0.446293i	$0.147256\pi$
$271$	−1.71463	+	8.06671i	−0.104157	+	0.490018i	−0.999044	+	0.0437253i	$0.986077\pi$
$272$	39.7274	+	20.2421i	2.40882	+	1.22736i
$273$	−4.32013	−	11.7105i	−0.261466	−	0.708754i
$274$			34.4291i			2.07994i
$275$	0.528728	+	0.0294295i	0.0318835	+	0.00177467i
$276$	1.93323	−	1.11615i	0.116367	−	0.0671844i
$277$	−9.97780	+	8.07986i	−0.599508	+	0.485472i	−0.880377	−	0.474274i	$-0.842711\pi$
$277$	−9.97780	+	8.07986i	−0.599508	+	0.485472i	0.280869	+	0.959746i	$0.409377\pi$
$278$	−6.23881	−	9.60693i	−0.374179	−	0.576185i
$279$	5.37192	+	16.5331i	0.321609	+	0.989809i
$280$	43.0627	−	7.32727i	2.57349	−	0.437888i
$281$	8.46995	−	26.0678i	0.505275	−	1.55508i	−0.295033	−	0.955487i	$-0.595331\pi$
$281$	8.46995	−	26.0678i	0.505275	−	1.55508i	0.800308	−	0.599589i	$-0.204669\pi$
$282$	38.0964	−	10.2079i	2.26861	−	0.607872i
$283$	13.3500	+	8.66959i	0.793575	+	0.515353i	0.876615	−	0.481193i	$-0.159796\pi$
$283$	13.3500	+	8.66959i	0.793575	+	0.515353i	−0.0830401	+	0.996546i	$0.526463\pi$
$284$	−15.4410	+	34.6811i	−0.916255	+	2.05794i
$285$	−0.203032	−	8.26579i	−0.0120266	−	0.489623i
$286$	−0.257020	+	0.353758i	−0.0151979	+	0.0209181i
$287$	4.85894	−	9.23514i	0.286814	−	0.545133i
$288$	9.63393	−	60.8263i	0.567685	−	3.58422i
$289$	−1.78903	−	4.01822i	−0.105237	−	0.236366i
$290$	−20.4555	−	21.6257i	−1.20119	−	1.26990i
$291$	29.5052	+	13.1366i	1.72963	+	0.770080i
$292$	−65.8660	−	3.45189i	−3.85452	−	0.202007i
$293$	16.2607	+	16.2607i	0.949961	+	0.949961i	0.998806	−	0.0488456i	$-0.0155542\pi$
$293$	16.2607	+	16.2607i	0.949961	+	0.949961i	−0.0488456	+	0.998806i	$0.515554\pi$
$294$	44.9973	−	30.9247i	2.62430	−	1.80357i
$295$	−10.6173	−	25.7504i	−0.618161	−	1.49925i
$296$	−3.72503	−	0.791780i	−0.216513	−	0.0460213i
$297$	−0.0481990	−	0.919691i	−0.00279679	−	0.0533659i
$298$	2.84659	+	3.51525i	0.164899	+	0.203633i
$299$	0.122421	−	0.212039i	0.00707978	−	0.0122625i
$300$	−42.5322	+	58.1430i	−2.45560	+	3.35689i
$301$	−15.5854	−	5.29066i	−0.898325	−	0.304949i
$302$	2.22742	+	14.0634i	0.128173	+	0.809255i
$303$	23.1634	−	15.0425i	1.33070	−	0.864169i
$304$	−7.98828	+	8.87188i	−0.458159	+	0.508837i
$305$	−6.41623	+	18.0259i	−0.367392	+	1.03216i
$306$	−53.1052	+	47.8161i	−3.03582	+	2.73347i
$307$	−7.08123	+	7.08123i	−0.404147	+	0.404147i	−0.879692	−	0.475544i	$-0.842251\pi$
$307$	−7.08123	+	7.08123i	−0.404147	+	0.404147i	0.475544	+	0.879692i	$0.342251\pi$
$308$	−1.25603	−	0.501117i	−0.0715690	−	0.0285538i
$309$	−11.7172	−	16.1274i	−0.666570	−	0.917455i
$310$	−13.6438	+	10.4342i	−0.774917	+	0.592621i
$311$	6.77650	+	0.712239i	0.384260	+	0.0403874i	0.294689	−	0.955593i	$-0.404784\pi$
$311$	6.77650	+	0.712239i	0.384260	+	0.0403874i	0.0895708	+	0.995980i	$0.471450\pi$
$312$	−12.4833	−	32.5201i	−0.706727	−	1.84109i
$313$	5.83431	−	7.20477i	0.329775	−	0.407238i	−0.585109	−	0.810954i	$-0.698948\pi$
$313$	5.83431	−	7.20477i	0.329775	−	0.407238i	0.914884	+	0.403717i	$0.132282\pi$
$314$	−16.1495	−	11.7333i	−0.911367	−	0.662147i
$315$	−6.88020	+	34.2968i	−0.387655	+	1.93241i
$316$	−24.1487	+	17.5451i	−1.35847	+	0.986987i
$317$	0.938869	−	17.9147i	0.0527321	−	1.00619i	−0.836279	−	0.548304i	$-0.815274\pi$
$317$	0.938869	−	17.9147i	0.0527321	−	1.00619i	0.889011	−	0.457885i	$-0.151393\pi$
$318$	25.5991	−	95.5371i	1.43553	−	5.35746i
$319$	0.112198	+	0.527848i	0.00628186	+	0.0295538i
$320$	17.4517	−	3.20521i	0.975579	−	0.179177i
$321$	−36.4216	+	11.8341i	−2.03285	+	0.660514i
$322$	1.03079	+	0.290721i	0.0574435	+	0.0162013i
$323$	5.65896	−	0.896291i	0.314873	−	0.0498710i
$324$	34.3641	+	19.8401i	1.90911	+	1.10223i
$325$	−0.851398	+	7.85532i	−0.0472271	+	0.435735i
$326$	26.8918	+	46.5780i	1.48940	+	2.57972i
$327$	12.0334	−	31.3482i	0.665450	−	1.73356i
$328$	13.2212	−	25.9481i	0.730018	−	1.43274i
$329$	11.4973	+	6.84031i	0.633867	+	0.377118i
$330$	1.70771	−	0.704116i	0.0940066	−	0.0387603i
$331$	−14.2559	−	15.8328i	−0.783577	−	0.870250i	0.210648	−	0.977562i	$-0.432442\pi$
$331$	−14.2559	−	15.8328i	−0.783577	−	0.870250i	−0.994225	+	0.107311i	$0.965776\pi$
$332$	−41.6965	−	11.1725i	−2.28839	−	0.613173i
$333$	1.66095	−	2.55764i	0.0910195	−	0.140158i
$334$	−2.22089	−	21.1304i	−0.121522	−	1.15620i
$335$	1.10175	+	4.62212i	0.0601949	+	0.252534i
$336$	62.1735	−	43.9391i	3.39184	−	2.39707i
$337$	−1.92468	−	0.304839i	−0.104844	−	0.0166057i	0.103792	−	0.994599i	$-0.466902\pi$
$337$	−1.92468	−	0.304839i	−0.104844	−	0.0166057i	−0.208636	+	0.977993i	$0.566902\pi$
$338$	21.3251	+	17.2687i	1.15993	+	0.939295i
$339$	−1.21730	+	11.5818i	−0.0661147	+	0.629040i
$340$	−43.8313	−	23.8906i	−2.37708	−	1.29565i
$341$	0.309677	−	0.0325483i	0.0167699	−	0.00176259i
$342$	−8.68648	−	17.0482i	−0.469711	−	0.921860i
$343$	18.1643	+	3.61357i	0.980780	+	0.195115i
$344$	−43.6840	−	14.1938i	−2.35528	−	0.765278i
$345$	−0.909759	+	0.492050i	−0.0489798	+	0.0264911i
$346$	−23.3567	−	21.0305i	−1.25567	−	1.13061i
$347$	−29.1369	+	1.52700i	−1.56415	+	0.0819737i	−0.814620	−	0.579996i	$-0.803054\pi$
$347$	−29.1369	+	1.52700i	−1.56415	+	0.0819737i	−0.749531	+	0.661969i	$0.769721\pi$
$348$	−68.5361	−	26.3085i	−3.67392	−	1.41029i
$349$	6.38042			0.341536			0.170768	−	0.985311i	$-0.445375\pi$
$349$	6.38042			0.341536			0.170768	+	0.985311i	$0.445375\pi$
$350$	−34.2207	+	4.84819i	−1.82917	+	0.259146i
$351$	13.7415			0.733466
$352$	−1.02984	−	0.395318i	−0.0548906	−	0.0210705i
$353$	6.33084	−	0.331785i	0.336957	−	0.0176591i	0.116893	−	0.993145i	$-0.462707\pi$
$353$	6.33084	−	0.331785i	0.336957	−	0.0176591i	0.220064	+	0.975485i	$0.429373\pi$
$354$	−72.2031	−	65.0120i	−3.83755	−	3.45535i
$355$	7.59825	−	15.8638i	0.403273	−	0.841962i
$356$	62.4095	+	20.2781i	3.30770	+	1.07474i
$357$	−36.4598	−	2.39001i	−1.92966	−	0.126493i
$358$	19.5639	+	38.3964i	1.03399	+	2.02931i
$359$	13.0750	−	1.37424i	0.690073	−	0.0725296i	0.247001	−	0.969015i	$-0.420555\pi$
$359$	13.0750	−	1.37424i	0.690073	−	0.0725296i	0.443073	+	0.896486i	$0.353888\pi$
$360$	−17.9454	+	95.9560i	−0.945806	+	5.05732i
$361$	1.82568	−	17.3702i	0.0960887	−	0.914223i
$362$	37.3314	+	30.2304i	1.96209	+	1.58887i
$363$	32.4022	+	5.13201i	1.70067	+	0.269360i
$364$	8.44772	−	18.3241i	0.442781	−	0.960445i
$365$	30.4616	+	2.44710i	1.59443	+	0.128087i
$366$	6.97654	+	66.3774i	0.364670	+	3.46960i
$367$	4.39708	−	6.77091i	0.229526	−	0.353439i	−0.705078	−	0.709130i	$-0.749088\pi$
$367$	4.39708	−	6.77091i	0.229526	−	0.353439i	0.934603	+	0.355691i	$0.115755\pi$
$368$	1.44250	+	0.386518i	0.0751957	+	0.0201486i
$369$	15.6048	+	17.3308i	0.812351	+	0.902208i
$370$	2.92882	+	0.708173i	0.152262	+	0.0368161i
$371$	29.2720	−	16.3928i	1.51973	−	0.851073i
$372$	−19.2311	+	37.7431i	−0.997086	+	1.95689i
$373$	−3.77983	+	9.84679i	−0.195712	+	0.509847i	−0.995958	−	0.0898253i	$-0.971369\pi$
$373$	−3.77983	+	9.84679i	−0.195712	+	0.509847i	0.800246	+	0.599672i	$0.204702\pi$
$374$	0.640001	+	1.10851i	0.0330936	+	0.0573199i
$375$	20.4478	−	26.3814i	1.05592	−	1.36233i
$376$	32.3330	+	18.6675i	1.66745	+	0.962702i
$377$	−7.95280	+	1.25960i	−0.409590	+	0.0648727i
$378$	14.7955	+	58.2593i	0.760997	+	2.99654i
$379$	−29.5616	+	9.60515i	−1.51848	+	0.493384i	−0.945343	−	0.326077i	$-0.894273\pi$
$379$	−29.5616	+	9.60515i	−1.51848	+	0.493384i	−0.573135	+	0.819461i	$0.694273\pi$
$380$	9.21628	−	9.68044i	0.472785	−	0.496596i
$381$	−6.04652	−	28.4466i	−0.309772	−	1.45736i
$382$	−17.3265	+	64.6635i	−0.886502	+	3.30847i
$383$	−0.680767	+	12.9898i	−0.0347856	+	0.663748i	0.924478	+	0.381235i	$0.124501\pi$
$383$	−0.680767	+	12.9898i	−0.0347856	+	0.663748i	−0.959264	+	0.282513i	$0.908832\pi$
$384$	−0.239540	+	0.174036i	−0.0122240	+	0.00888122i
$385$	0.575281	+	0.248272i	0.0293190	+	0.0126531i
$386$	−1.17184	−	0.851394i	−0.0596453	−	0.0433348i
$387$	23.1478	−	28.5852i	1.17667	−	1.45307i
$388$	18.7105	+	48.7425i	0.949881	+	2.47452i
$389$	8.02779	+	0.843755i	0.407025	+	0.0427801i	0.305829	−	0.952086i	$-0.401066\pi$
$389$	8.02779	+	0.843755i	0.407025	+	0.0427801i	0.101196	+	0.994867i	$0.467733\pi$
$390$	9.15811	+	25.9956i	0.463739	+	1.31634i
$391$	−0.421275	−	0.579836i	−0.0213048	−	0.0293236i
$392$	50.8192	+	9.41965i	2.56676	+	0.475764i
$393$	−17.3752	+	17.3752i	−0.876461	+	0.876461i
$394$	−6.90575	+	6.21797i	−0.347907	+	0.313257i
$395$	11.4105	−	7.81503i	0.574127	−	0.393217i
$396$	2.02220	−	2.24588i	0.101619	−	0.112860i
$397$	17.0578	−	11.0775i	0.856108	−	0.555963i	−0.0403030	−	0.999188i	$-0.512832\pi$
$397$	17.0578	−	11.0775i	0.856108	−	0.555963i	0.896411	+	0.443225i	$0.146166\pi$
$398$	1.06419	+	6.71904i	0.0533431	+	0.336795i
$399$	3.14477	−	9.26395i	0.157436	−	0.463777i
$400$	−47.6242	+	7.38466i	−2.38121	+	0.369233i
$401$	−14.0818	+	24.3904i	−0.703213	+	1.21800i	0.264119	+	0.964490i	$0.414919\pi$
$401$	−14.0818	+	24.3904i	−0.703213	+	1.21800i	−0.967333	+	0.253511i	$0.918415\pi$
$402$	10.4308	+	12.8810i	0.520242	+	0.642445i
$403$	0.243159	+	4.63975i	0.0121126	+	0.231122i
$404$	43.6719	+	9.28275i	2.17276	+	0.461834i
$405$	−15.6603	−	9.63162i	−0.778167	−	0.478599i
$406$	−13.9031	−	32.3611i	−0.689999	−	1.60605i
$407$	−0.0386260	−	0.0386260i	−0.00191462	−	0.00191462i
$408$	−101.828	−	5.33656i	−5.04122	−	0.264199i
$409$	−3.53088	−	1.57205i	−0.174591	−	0.0777328i	0.317580	−	0.948231i	$-0.397130\pi$
$409$	−3.53088	−	1.57205i	−0.174591	−	0.0777328i	−0.492171	+	0.870499i	$0.663796\pi$
$410$	−11.0277	+	20.2322i	−0.544621	+	0.999199i
$411$	−16.0014	−	35.9398i	−0.789293	−	1.77278i
$412$	5.04110	−	31.8283i	0.248357	−	1.56807i
$413$	−1.29359	−	32.9311i	−0.0636536	−	1.62044i
$414$	−1.40685	+	1.93636i	−0.0691427	+	0.0951668i
$415$	19.1680	+	5.71165i	0.940920	+	0.280374i
$416$	6.69464	−	15.0364i	0.328232	−	0.737220i
$417$	10.9775	+	7.12890i	0.537572	+	0.349104i
$418$	−0.331046	+	0.0887034i	−0.0161920	+	0.00433862i
$419$	2.14134	−	6.59038i	0.104612	−	0.321961i	−0.885028	−	0.465539i	$-0.845861\pi$
$419$	2.14134	−	6.59038i	0.104612	−	0.321961i	0.989639	+	0.143577i	$0.0458606\pi$
$420$	−70.9496	+	47.2399i	−3.46198	+	2.30507i
$421$	7.05679	+	21.7186i	0.343927	+	1.05850i	0.962156	+	0.272500i	$0.0878504\pi$
$421$	7.05679	+	21.7186i	0.343927	+	1.05850i	−0.618229	+	0.785998i	$0.712150\pi$
$422$	−5.19147	−	7.99416i	−0.252717	−	0.389149i
$423$	−23.2349	+	18.8152i	−1.12972	+	0.914828i
$424$	81.0838	−	46.8138i	3.93778	−	2.27348i
$425$	19.9929	+	11.6295i	0.969798	+	0.564116i
$426$		−	61.3564i		−	2.97273i
$427$	−14.4767	+	17.4060i	−0.700575	+	0.842335i
$428$	−55.1595	−	28.1051i	−2.66623	−	1.35851i
$429$	0.103884	−	0.488735i	0.00501556	−	0.0235963i
$430$	34.2387	+	12.1871i	1.65114	+	0.587714i
$431$	−5.41482	+	1.15095i	−0.260823	+	0.0554395i	−0.336467	−	0.941695i	$-0.609232\pi$
$431$	−5.41482	+	1.15095i	−0.260823	+	0.0554395i	0.0756443	+	0.997135i	$0.475899\pi$
$432$	21.6929	+	80.9589i	1.04370	+	3.89514i
$433$	−26.6331	+	13.5702i	−1.27990	+	0.652143i	−0.955839	−	0.293892i	$-0.905049\pi$
$433$	−26.6331	+	13.5702i	−1.27990	+	0.652143i	−0.324064	+	0.946035i	$0.605049\pi$
$434$	−19.4092	+	6.02654i	−0.931671	+	0.289283i
$435$	31.4039	+	13.0676i	1.50570	+	0.626545i
$436$	49.5881	−	22.0780i	2.37484	−	1.05735i
$437$	0.179157	−	0.0687718i	0.00857022	−	0.00328980i
$438$	99.5191	−	38.2018i	4.75521	−	1.82535i
$439$	−6.73922	+	3.00050i	−0.321646	+	0.143206i	−0.561207	−	0.827675i	$-0.689663\pi$
$439$	−6.73922	+	3.00050i	−0.321646	+	0.143206i	0.239562	+	0.970881i	$0.422996\pi$
$440$	1.61438	+	0.671769i	0.0769627	+	0.0320253i
$441$	−21.6263	+	35.2896i	−1.02982	+	1.68046i
$442$	−17.0172	+	8.67067i	−0.809424	+	0.412422i
$443$	2.33943	+	8.73088i	0.111150	+	0.414817i	0.998970	−	0.0453736i	$-0.0144478\pi$
$443$	2.33943	+	8.73088i	0.111150	+	0.414817i	−0.887820	+	0.460190i	$0.847781\pi$
$444$	7.26879	−	1.54503i	0.344961	−	0.0733238i
$445$	−28.6440	−	10.1957i	−1.35786	−	0.483322i
$446$	−0.430832	+	2.02690i	−0.0204005	+	0.0959767i
$447$	−4.60526	−	2.34650i	−0.217821	−	0.110986i
$448$	20.6912	+	3.55558i	0.977569	+	0.167985i
$449$		−	1.97023i		−	0.0929809i	−0.998919	−	0.0464905i	$-0.985196\pi$
$449$		−	1.97023i		−	0.0929809i	0.998919	−	0.0464905i	$-0.0148037\pi$
$450$	16.3041	−	75.4996i	0.768582	−	3.55908i
$451$	0.361763	−	0.208864i	0.0170347	−	0.00983501i
$452$	−14.6303	+	11.8474i	−0.688151	+	0.557254i
$453$	−8.86132	−	13.6452i	−0.416341	−	0.641109i
$454$	6.38443	+	19.6493i	0.299636	+	0.922186i
$455$	−4.14861	+	8.37808i	−0.194490	+	0.392771i
$456$	8.43680	−	25.9658i	0.395089	−	1.21596i
$457$	1.96739	−	0.527159i	0.0920304	−	0.0246595i	−0.212510	−	0.977159i	$-0.568164\pi$
$457$	1.96739	−	0.527159i	0.0920304	−	0.0246595i	0.304540	+	0.952499i	$0.401497\pi$
$458$	−46.0014	−	29.8736i	−2.14950	−	1.39590i
$459$	16.3609	−	36.7473i	0.763664	−	1.71522i
$460$	−1.60236	−	0.477469i	−0.0747105	−	0.0222621i
$461$	−15.8458	+	21.8099i	−0.738014	+	1.01579i	0.260716	+	0.965415i	$0.416041\pi$
$461$	−15.8458	+	21.8099i	−0.738014	+	1.01579i	−0.998730	+	0.0503737i	$0.983959\pi$
$462$	2.18393	−	0.0857886i	0.101605	−	0.00399125i
$463$	0.995965	−	6.28827i	0.0462864	−	0.292241i	−0.953677	−	0.300834i	$-0.902735\pi$
$463$	0.995965	−	6.28827i	0.0462864	−	0.292241i	0.999963	+	0.00859262i	$0.00273515\pi$
$464$	−19.9757	−	44.8661i	−0.927347	−	2.08285i
$465$	9.39308	−	17.2332i	0.435594	−	0.799170i
$466$	−41.3775	−	18.4225i	−1.91678	−	0.853404i
$467$	−23.9414	−	1.25472i	−1.10788	−	0.0580613i	−0.510392	−	0.859942i	$-0.670500\pi$
$467$	−23.9414	−	1.25472i	−1.10788	−	0.0580613i	−0.597484	+	0.801881i	$0.703833\pi$
$468$	31.8855	+	31.8855i	1.47391	+	1.47391i
$469$	−0.660864	+	5.58321i	−0.0305159	+	0.257809i
$470$	−25.1625	−	15.4758i	−1.16066	−	0.713845i
$471$	22.3113	+	4.74241i	1.02805	+	0.218519i
$472$	−4.81346	−	91.8463i	−0.221558	−	4.22757i
$473$	−0.414626	−	0.512021i	−0.0190645	−	0.0235427i
$474$	24.1215	−	41.7797i	1.10794	−	1.91900i
$475$	−4.39324	+	4.36483i	−0.201575	+	0.200272i
$476$	−38.9441	−	44.4080i	−1.78500	−	2.03544i
$477$	11.7289	+	74.0535i	0.537031	+	3.39068i
$478$	22.4723	−	14.5937i	1.02786	−	0.667499i
$479$	1.12148	−	1.24553i	0.0512418	−	0.0569098i	−0.716979	−	0.697095i	$-0.754476\pi$
$479$	1.12148	−	1.24553i	0.0512418	−	0.0569098i	0.768221	+	0.640185i	$0.221142\pi$
$480$	−57.3655	+	39.2894i	−2.61837	+	1.79331i
$481$	0.605709	−	0.545383i	0.0276179	−	0.0248673i
$482$	50.9766	−	50.9766i	2.32192	−	2.32192i
$483$	−1.21114	+	0.175596i	−0.0551086	+	0.00798990i
$484$	31.1717	+	42.9041i	1.41689	+	1.95019i
$485$	−8.03803	−	22.8162i	−0.364988	−	1.03603i
$486$	4.00326	+	0.420760i	0.181592	+	0.0190861i
$487$	11.0504	+	28.7873i	0.500743	+	1.30448i	0.918320	+	0.395838i	$0.129546\pi$
$487$	11.0504	+	28.7873i	0.500743	+	1.30448i	−0.417578	+	0.908641i	$0.637121\pi$
$488$	−39.7606	+	49.1002i	−1.79988	+	2.22266i
$489$	−49.7196	−	36.1234i	−2.24840	−	1.63356i
$490$	−39.9871	−	8.56803i	−1.80643	−	0.387064i
$491$	−5.12812	+	3.72580i	−0.231429	+	0.168143i	−0.697456	−	0.716627i	$-0.745685\pi$
$491$	−5.12812	+	3.72580i	−0.231429	+	0.168143i	0.466027	+	0.884770i	$0.345685\pi$
$492$	−2.97410	+	56.7493i	−0.134083	+	2.55846i
$493$	−6.10040	+	22.7670i	−0.274748	+	1.02537i
$494$	−1.06321	−	5.00201i	−0.0478360	−	0.225051i
$495$	−0.965516	+	1.01414i	−0.0433967	+	0.0455823i
$496$	−26.9515	+	8.75709i	−1.21016	+	0.393205i
$497$	14.9080	−	14.5225i	0.668715	−	0.651422i
$498$	68.9087	−	10.9141i	3.08787	−	0.489071i
$499$	−36.2714	−	20.9413i	−1.62373	−	0.937462i	−0.985910	−	0.167277i	$-0.946503\pi$
$499$	−36.2714	−	20.9413i	−1.62373	−	0.937462i	−0.637821	−	0.770184i	$-0.720164\pi$
$500$	53.5289	−	6.78242i	2.39389	−	0.303319i
$501$	12.1390	+	21.0254i	0.542331	+	0.939344i
$502$	0.508055	−	1.32353i	0.0226756	−	0.0590719i
$503$	−16.7270	+	32.8287i	−0.745822	+	1.46376i	0.135268	+	0.990809i	$0.456811\pi$
$503$	−16.7270	+	32.8287i	−0.745822	+	1.46376i	−0.881090	+	0.472949i	$0.843189\pi$
$504$	−59.0578	+	99.2653i	−2.63064	+	4.42163i
$505$	−20.1073	−	4.86183i	−0.894761	−	0.216349i
$506$	0.0286870	+	0.0318602i	0.00127529	+	0.00141636i
$507$	−30.2867	−	8.11531i	−1.34508	−	0.360413i
$508$	25.6048	−	39.4280i	1.13603	−	1.74933i
$509$	−4.22239	−	40.1734i	−0.187154	−	1.78065i	−0.536739	−	0.843748i	$-0.680344\pi$
$509$	−4.22239	−	40.1734i	−0.187154	−	1.78065i	0.349585	−	0.936905i	$-0.386323\pi$
$510$	80.4210	+	6.46053i	3.56110	+	0.286077i
$511$	32.8372	+	15.1385i	1.45263	+	0.669688i
$512$	−41.4263	−	6.56128i	−1.83080	−	0.289970i
$513$	8.37012	+	6.77799i	0.369550	+	0.299255i
$514$	−4.69767	+	44.6953i	−0.207205	+	1.97143i
$515$	−2.74475	+	14.6765i	−0.120948	+	0.646722i
$516$	89.1379	−	9.36877i	3.92408	−	0.412437i
$517$	0.243126	+	0.477162i	0.0106927	+	0.0209855i
$518$	2.96441	+	1.98079i	0.130249	+	0.0870310i
$519$	34.1559	+	11.0979i	1.49928	+	0.487145i
$520$	−11.2704	+	23.5305i	−0.494238	+	1.03188i
$521$	11.8397	+	10.6605i	0.518707	+	0.467046i	0.886412	−	0.462896i	$-0.153190\pi$
$521$	11.8397	+	10.6605i	0.518707	+	0.467046i	−0.367705	+	0.929942i	$0.619856\pi$
$522$	78.6044	−	4.11948i	3.44042	−	0.180305i
$523$	12.3853	+	4.75426i	0.541570	+	0.207889i	0.613747	−	0.789503i	$-0.289661\pi$
$523$	12.3853	+	4.75426i	0.541570	+	0.207889i	−0.0721772	+	0.997392i	$0.522995\pi$
$524$	−39.7220			−1.73526
$525$	33.4690	−	20.9655i	1.46071	−	0.915009i
$526$	52.6279			2.29469
$527$	12.6971	+	4.87395i	0.553093	+	0.212312i
$528$	3.04341	−	0.159498i	0.132447	−	0.00694128i
$529$	17.0745	+	15.3739i	0.742369	+	0.668432i
$530$	−65.1611	+	35.2429i	−2.83042	+	1.53085i
$531$	70.0464	+	22.7595i	3.03976	+	0.987677i
$532$	14.1840	−	6.99463i	0.614955	−	0.303256i
$533$	2.82967	+	5.55354i	0.122567	+	0.240550i
$534$	−105.477	+	11.0861i	−4.56442	+	0.479740i
$535$	25.1853	+	13.7274i	1.08886	+	0.593489i
$536$	−1.64005	+	15.6040i	−0.0708392	+	0.673990i
$537$	−38.2677	−	30.9886i	−1.65137	−	1.33726i
$538$	6.39869	+	1.01345i	0.275867	+	0.0436931i
$539$	0.537759	+	0.510331i	0.0231629	+	0.0219815i
$540$	−21.7581	−	91.2810i	−0.936320	−	3.92811i
$541$	−3.36061	−	31.9740i	−0.144484	−	1.37467i	−0.791021	−	0.611789i	$-0.790450\pi$
$541$	−3.36061	−	31.9740i	−0.144484	−	1.37467i	0.646537	−	0.762882i	$-0.276216\pi$
$542$	11.7351	−	18.0704i	0.504065	−	0.776191i
$543$	−53.0195	−	14.2065i	−2.27528	−	0.609661i
$544$	−32.2394	−	35.8054i	−1.38225	−	1.53515i
$545$	−23.2513	+	9.58684i	−0.995975	+	0.410655i
$546$	−0.427139	+	32.6085i	−0.0182799	+	1.39552i
$547$	0.393959	−	0.773188i	0.0168445	−	0.0330591i	−0.882431	−	0.470442i	$-0.844095\pi$
$547$	0.393959	−	0.773188i	0.0168445	−	0.0330591i	0.899275	+	0.437383i	$0.144095\pi$
$548$	22.7909	−	59.3723i	0.973579	−	2.53626i
$549$	−25.2972	−	43.8161i	−1.07966	−	1.87003i
$550$	−1.26209	−	0.566829i	−0.0538155	−	0.0241697i
$551$	−5.46546	−	3.15548i	−0.232836	−	0.134428i
$552$	−3.37323	+	0.534267i	−0.143574	+	0.0227399i
$553$	15.8607	−	4.02796i	0.674465	−	0.171286i
$554$	31.9024	−	10.3657i	1.35540	−	0.440397i
$555$	−3.38647	+	0.621965i	−0.143748	+	0.0264009i
$556$	4.39926	+	20.6969i	0.186570	+	0.877743i
$557$	8.40723	−	31.3762i	0.356226	−	1.32945i	−0.522709	−	0.852511i	$-0.675079\pi$
$557$	8.40723	−	31.3762i	0.356226	−	1.32945i	0.878935	−	0.476941i	$-0.158255\pi$
$558$	2.37702	−	45.3562i	0.100627	−	1.92008i
$559$	7.95314	−	5.77829i	0.336382	−	0.244396i
$560$	−55.9093	−	11.2158i	−2.36260	−	0.473955i
$561$	−1.18328	−	0.859705i	−0.0499582	−	0.0362968i
$562$	−45.0666	+	55.6527i	−1.90102	+	2.34757i
$563$	−5.26563	−	13.7174i	−0.221920	−	0.578121i	0.776743	−	0.629818i	$-0.216870\pi$
$563$	−5.26563	−	13.7174i	−0.221920	−	0.578121i	−0.998663	+	0.0516965i	$0.983537\pi$
$564$	−72.4540	−	7.61522i	−3.05086	−	0.320659i
$565$	6.92867	−	5.29872i	0.291491	−	0.222919i
$566$	−24.4452	−	33.6459i	−1.02751	−	1.41424i
$567$	−13.4674	−	17.0836i	−0.565577	−	0.717443i
$568$	41.0696	−	41.0696i	1.72324	−	1.72324i
$569$	31.3512	−	28.2287i	1.31431	−	1.18341i	0.344712	−	0.938708i	$-0.387977\pi$
$569$	31.3512	−	28.2287i	1.31431	−	1.18341i	0.969598	−	0.244702i	$-0.0786901\pi$
$570$	−7.24402	+	20.3515i	−0.303418	+	0.852431i
$571$	−15.1300	+	16.8035i	−0.633169	+	0.703206i	−0.971290	−	0.237897i	$-0.923542\pi$
$571$	−15.1300	+	16.8035i	−0.633169	+	0.703206i	0.338121	+	0.941103i	$0.390209\pi$
$572$	0.677403	−	0.439911i	0.0283236	−	0.0183936i
$573$	−11.9665	−	75.5537i	−0.499909	−	3.15630i
$574$	−20.4985	+	17.9764i	−0.855589	+	0.750319i
$575$	0.735990	+	0.241780i	0.0306929	+	0.0100829i
$576$	−23.4592	+	40.6326i	−0.977468	+	1.69302i
$577$	16.1625	+	19.9590i	0.672854	+	0.830906i	0.993203	−	0.116394i	$-0.0371335\pi$
$577$	16.1625	+	19.9590i	0.672854	+	0.830906i	−0.320349	+	0.947300i	$0.603800\pi$
$578$	0.601435	+	11.4761i	0.0250164	+	0.477341i
$579$	1.61896	+	0.344121i	0.0672818	+	0.0143012i
$580$	20.9596	+	50.8340i	0.870300	+	2.11077i
$581$	18.9618	+	14.1597i	0.786670	+	0.587444i
$582$	−59.6676	−	59.6676i	−2.47330	−	2.47330i
$583$	1.34115	+	0.0702866i	0.0555447	+	0.00291097i
$584$	92.1849	+	41.0434i	3.81464	+	1.69839i
$585$	−14.3572	−	15.1786i	−0.593598	−	0.627558i
$586$	−24.4373	−	54.8870i	−1.00949	−	2.26736i
$587$	5.73052	−	36.1811i	0.236524	−	1.49335i	−0.528269	−	0.849077i	$-0.677159\pi$
$587$	5.73052	−	36.1811i	0.236524	−	1.49335i	0.764793	−	0.644276i	$-0.222841\pi$
$588$	−98.0682	+	23.5424i	−4.04427	+	0.970871i
$589$	−2.14044	+	2.94607i	−0.0881955	+	0.121391i
$590$	1.78695	+	72.7497i	0.0735676	+	2.99506i
$591$	4.31888	−	9.70036i	0.177655	−	0.399020i
$592$	4.16936	+	2.70761i	0.171360	+	0.111282i
$593$	16.1210	−	4.31960i	0.662009	−	0.177385i	0.0878564	−	0.996133i	$-0.471998\pi$
$593$	16.1210	−	4.31960i	0.662009	−	0.177385i	0.574152	+	0.818748i	$0.305332\pi$
$594$	−0.743541	+	2.28838i	−0.0305078	+	0.0938935i
$595$	17.4651	+	21.0693i	0.716001	+	0.863758i
$596$	−2.58192	−	7.94633i	−0.105760	−	0.325494i
$597$	−4.23367	−	6.51927i	−0.173272	−	0.266816i
$598$	−0.497133	+	0.402571i	−0.0203293	+	0.0164623i
$599$	17.1188	−	9.88355i	0.699455	−	0.403831i	−0.107689	−	0.994185i	$-0.534345\pi$
$599$	17.1188	−	9.88355i	0.699455	−	0.403831i	0.807145	+	0.590354i	$0.201012\pi$
$600$	92.6281	−	59.7271i	3.78153	−	2.43835i
$601$			23.8371i			0.972336i	0.873865	+	0.486168i	$0.161606\pi$
$601$			23.8371i			0.972336i	−0.873865	+	0.486168i	$0.838394\pi$
$602$	33.0612	+	27.4972i	1.34748	+	1.12070i
$603$	−11.1950	−	5.70414i	−0.455896	−	0.232291i
$604$	5.46834	−	25.7265i	0.222503	−	1.04680i
$605$	−13.8847	−	20.2727i	−0.564493	−	0.824202i
$606$	−70.5830	+	15.0029i	−2.86724	+	0.609451i
$607$	1.19982	+	4.47778i	0.0486991	+	0.181747i	0.985991	−	0.166797i	$-0.0533426\pi$
$607$	1.19982	+	4.47778i	0.0486991	+	0.181747i	−0.937292	+	0.348545i	$0.886676\pi$
$608$	11.4945	−	5.85674i	0.466164	−	0.237522i
$609$	29.5535	+	27.3194i	1.19757	+	1.10704i
$610$	32.5277	−	37.9602i	1.31701	−	1.53696i
$611$	−7.29979	+	3.25008i	−0.295318	+	0.131484i
$612$	123.232	−	47.3042i	4.98135	−	1.91216i
$613$	−27.2478	+	10.4595i	−1.10053	+	0.422454i	−0.839766	−	0.542949i	$-0.817308\pi$
$613$	−27.2478	+	10.4595i	−1.10053	+	0.422454i	−0.260764	+	0.965403i	$0.583974\pi$
$614$	23.9022	−	10.6420i	0.964616	−	0.429475i
$615$	2.10839	−	26.2453i	0.0850185	−	1.05831i
$616$	1.51926	+	1.40441i	0.0612126	+	0.0565853i
$617$	−15.1045	+	7.69612i	−0.608084	+	0.309834i	−0.730783	−	0.682610i	$-0.760845\pi$
$617$	−15.1045	+	7.69612i	−0.608084	+	0.309834i	0.122699	+	0.992444i	$0.460845\pi$
$618$	13.4799	+	50.3077i	0.542242	+	2.02367i
$619$	−1.80856	+	0.384422i	−0.0726924	+	0.0154512i	−0.244114	−	0.969746i	$-0.578497\pi$
$619$	−1.80856	+	0.384422i	−0.0726924	+	0.0154512i	0.171422	+	0.985198i	$0.445164\pi$
$620$	30.4356	−	8.96177i	1.22232	−	0.359913i
$621$	0.280116	−	1.31784i	0.0112407	−	0.0528832i
$622$	−15.8620	−	8.08208i	−0.636007	−	0.324062i
$623$	−27.6589	−	23.0041i	−1.10813	−	0.921639i
$624$			45.4728i			1.82037i
$625$	−24.8795	+	2.45186i	−0.995179	+	0.0980743i
$626$	−20.9765	+	12.1108i	−0.838390	+	0.484044i
$627$	0.304346	−	0.246454i	0.0121544	−	0.00984243i
$628$	20.0824	+	30.9242i	0.801376	+	1.23401i
$629$	−0.737284	−	2.26913i	−0.0293974	−	0.0904760i
$630$	48.8938	−	77.2128i	1.94798	−	3.07623i
$631$	−14.8852	+	45.8121i	−0.592572	+	1.82375i	−0.0261130	+	0.999659i	$0.508313\pi$
$631$	−14.8852	+	45.8121i	−0.592572	+	1.82375i	−0.566459	+	0.824090i	$0.691687\pi$
$632$	44.1116	−	11.8197i	1.75467	−	0.470161i
$633$	9.13467	+	5.93213i	0.363071	+	0.235781i
$634$	−19.0635	+	42.8173i	−0.757109	+	1.70049i
$635$	−12.3668	+	17.9314i	−0.490762	+	0.711587i
$636$	−107.388	+	147.806i	−4.25820	+	5.86091i
$637$	−8.02411	+	7.61434i	−0.317927	+	0.301691i
$638$	0.220557	−	1.39255i	0.00873195	−	0.0551314i
$639$	18.9178	+	42.4901i	0.748377	+	1.68088i
$640$	0.217989	+	0.0407677i	0.00861677	+	0.00161148i
$641$	27.7155	+	12.3398i	1.09470	+	0.487391i	0.872998	−	0.487724i	$-0.162173\pi$
$641$	27.7155	+	12.3398i	1.09470	+	0.487391i	0.221700	+	0.975115i	$0.428839\pi$
$642$	99.9175	+	5.23645i	3.94343	+	0.206666i
$643$	15.1791	+	15.1791i	0.598605	+	0.598605i	0.939941	−	0.341336i	$-0.110879\pi$
$643$	15.1791	+	15.1791i	0.598605	+	0.598605i	−0.341336	+	0.939941i	$0.610879\pi$
$644$	−1.58513	−	1.18369i	−0.0624628	−	0.0466440i
$645$	−41.4052	+	3.19110i	−1.63033	+	0.125649i
$646$	−14.6422	−	3.11229i	−0.576089	−	0.122452i
$647$	−1.04548	−	19.9489i	−0.0411019	−	0.784271i	−0.938968	−	0.344003i	$-0.888217\pi$
$647$	−1.04548	−	19.9489i	−0.0411019	−	0.784271i	0.897866	−	0.440268i	$-0.145117\pi$
$648$	−38.2049	−	47.1791i	−1.50083	−	1.85337i
$649$	0.659624	−	1.14250i	0.0258925	−	0.0448471i
$650$	9.43159	−	18.3630i	0.369938	−	0.720258i
$651$	17.4599	−	15.3117i	0.684309	−	0.600113i
$652$	−15.5414	−	98.1244i	−0.608647	−	3.84285i
$653$	−37.0603	+	24.0672i	−1.45028	+	0.941824i	−0.451511	+	0.892266i	$0.649115\pi$
$653$	−37.0603	+	24.0672i	−1.45028	+	0.941824i	−0.998771	+	0.0495582i	$0.984219\pi$
$654$	−58.7024	+	65.1956i	−2.29545	+	2.54935i
$655$	18.3974	+	0.511613i	0.718845	+	0.0199904i
$656$	−28.2520	+	25.4382i	−1.10306	+	0.993196i
$657$	−57.1396	+	57.1396i	−2.22923	+	2.22923i
$658$	−21.6390	−	27.4494i	−0.843575	−	1.07009i
$659$	−20.2475	−	27.8683i	−0.788730	−	1.08559i	−0.994265	−	0.106944i	$-0.965893\pi$
$659$	−20.2475	−	27.8683i	−0.788730	−	1.08559i	0.205535	−	0.978650i	$-0.434107\pi$
$660$	−3.41103	+	0.0837850i	−0.132774	+	0.00326133i
$661$	−25.7734	−	2.70889i	−1.00247	−	0.105364i	−0.410952	−	0.911657i	$-0.634804\pi$
$661$	−25.7734	−	2.70889i	−1.00247	−	0.105364i	−0.591516	+	0.806293i	$0.701470\pi$
$662$	19.9480	+	51.9662i	0.775300	+	2.01973i
$663$	13.7340	−	16.9601i	0.533386	−	0.658677i
$664$	53.4302	+	38.8193i	2.07349	+	1.50648i
$665$	−6.65946	+	3.05690i	−0.258243	+	0.118542i
$666$	−6.44600	+	4.68329i	−0.249777	+	0.181474i
$667$	−0.0413168	+	0.788371i	−0.00159979	+	0.0305259i
$668$	−10.1577	+	37.9091i	−0.393014	+	1.46675i
$669$	−0.492298	−	2.31608i	−0.0190333	−	0.0895449i
$670$	1.64037	−	12.3056i	0.0633729	−	0.475405i
$671$	−0.861899	+	0.280048i	−0.0332732	+	0.0108111i
$672$	−79.7382	+	20.2502i	−3.07597	+	0.781169i
$673$	48.8149	−	7.73152i	1.88168	−	0.298028i	0.893230	−	0.449600i	$-0.148434\pi$
$673$	48.8149	−	7.73152i	1.88168	−	0.298028i	0.988446	+	0.151572i	$0.0484336\pi$
$674$	4.40914	+	2.54562i	0.169834	+	0.0980536i
$675$	8.90167	+	42.5574i	0.342625	+	1.63803i
$676$	−25.3434	−	43.8961i	−0.974748	−	1.68831i
$677$	−9.74806	+	25.3946i	−0.374648	+	0.975992i	0.608560	+	0.793508i	$0.291747\pi$
$677$	−9.74806	+	25.3946i	−0.374648	+	0.975992i	−0.983209	+	0.182485i	$0.941586\pi$
$678$	13.8132	−	27.1100i	0.530494	−	1.04115i
$679$	0.374899	−	28.6204i	0.0143873	−	1.09835i
$680$	49.5062	+	58.1551i	1.89848	+	2.23015i
$681$	−15.7969	−	17.5442i	−0.605338	−	0.672295i
$682$	−0.785819	−	0.210560i	−0.0300906	−	0.00806274i
$683$	10.0098	−	15.4137i	0.383013	−	0.589789i	−0.593608	−	0.804754i	$-0.702297\pi$
$683$	10.0098	−	15.4137i	0.383013	−	0.589789i	0.976622	+	0.214965i	$0.0689639\pi$
$684$	3.69436	+	35.1495i	0.141257	+	1.34397i
$685$	−11.3204	+	27.2050i	−0.432530	+	1.03945i
$686$	−40.9219	−	25.8212i	−1.56240	−	0.985858i
$687$	61.9041	+	9.80465i	2.36179	+	0.374071i
$688$	46.5984	+	37.7346i	1.77655	+	1.43862i
$689$	−2.09461	+	19.9289i	−0.0797982	+	0.759230i
$690$	2.67973	−	0.348373i	0.102016	−	0.0132623i
$691$	−24.2574	+	2.54955i	−0.922793	+	0.0969895i	−0.553995	−	0.832520i	$-0.686897\pi$
$691$	−24.2574	+	2.54955i	−0.922793	+	0.0969895i	−0.368798	+	0.929509i	$0.620231\pi$
$692$	26.3568	+	51.7281i	1.00194	+	1.96641i
$693$	−1.48595	+	0.732772i	−0.0564464	+	0.0278357i
$694$	72.4987	+	23.5562i	2.75201	+	0.894183i
$695$	−1.77096	−	9.64250i	−0.0671763	−	0.365761i
$696$	83.4668	+	75.1539i	3.16380	+	2.84870i
$697$	18.2203	−	0.954884i	0.690142	−	0.0361688i
$698$	−15.5627	−	5.97397i	−0.589058	−	0.226118i
$699$	51.7553			1.95756
$700$	62.2223	+	14.2923i	2.35178	+	0.540200i
$701$	−8.02401			−0.303063			−0.151531	−	0.988452i	$-0.548420\pi$
$701$	−8.02401			−0.303063			−0.151531	+	0.988452i	$0.548420\pi$
$702$	−33.5174	−	12.8661i	−1.26503	−	0.485600i
$703$	0.637955	−	0.0334338i	0.0240609	−	0.00126098i
$704$	0.624545	+	0.562343i	0.0235384	+	0.0211941i
$705$	33.4592	+	4.46021i	1.26015	+	0.167981i
$706$	−15.7524	−	5.11828i	−0.592851	−	0.192629i
$707$	−20.3516	−	13.5988i	−0.765401	−	0.511434i
$708$	81.4772	+	159.908i	3.06210	+	6.00971i
$709$	2.50116	−	0.262883i	0.0939331	−	0.00987276i	−0.0574453	−	0.998349i	$-0.518295\pi$
$709$	2.50116	−	0.262883i	0.0939331	−	0.00987276i	0.151378	+	0.988476i	$0.451629\pi$
$710$	−33.3864	+	31.5798i	−1.25297	+	1.18517i
$711$	−3.82267	+	36.3702i	−0.143361	+	1.36399i
$712$	−78.0225	−	63.1814i	−2.92402	−	2.36782i
$713$	0.449921	+	0.0712604i	0.0168497	+	0.00266872i
$714$	86.6928	+	39.9668i	3.24440	+	1.49572i
$715$	−0.319408	+	0.195021i	−0.0119452	+	0.00729339i
$716$	−8.32054	−	79.1646i	−0.310953	−	2.95852i
$717$	−16.6757	+	25.6784i	−0.622766	+	0.958976i
$718$	−33.1785	−	8.89015i	−1.23821	−	0.331777i
$719$	26.3473	+	29.2617i	0.982589	+	1.09128i	0.995818	+	0.0913630i	$0.0291224\pi$
$719$	26.3473	+	29.2617i	0.982589	+	1.09128i	−0.0132288	+	0.999912i	$0.504211\pi$
$720$	66.7608	−	108.548i	2.48803	−	4.04535i
$721$	−9.03288	+	15.1826i	−0.336402	+	0.565430i
$722$	−20.7168	+	40.6590i	−0.771000	+	1.51317i
$723$	−29.5213	+	76.9056i	−1.09791	+	2.86015i
$724$	−44.3658	−	76.8439i	−1.64884	−	2.85588i
$725$	−9.05278	−	23.8139i	−0.336212	−	0.884426i
$726$	−74.2284	−	42.8558i	−2.75487	−	1.59053i
$727$	28.5317	−	4.51898i	1.05818	−	0.167600i	0.396995	−	0.917821i	$-0.370053\pi$
$727$	28.5317	−	4.51898i	1.05818	−	0.167600i	0.661187	+	0.750221i	$0.270053\pi$
$728$	−22.1128	+	21.5410i	−0.819554	+	0.798361i
$729$	−27.8335	+	9.04365i	−1.03087	+	0.334950i
$730$	−72.0089	−	34.4900i	−2.66517	−	1.27653i
$731$	−5.98304	−	28.1480i	−0.221291	−	1.04109i
$732$	31.9087	−	119.085i	1.17938	−	4.40151i
$733$	0.490850	−	9.36598i	0.0181300	−	0.345940i	−0.974471	−	0.224515i	$-0.927920\pi$
$733$	0.490850	−	9.36598i	0.0181300	−	0.345940i	0.992601	−	0.121425i	$-0.0387465\pi$
$734$	−17.0647	+	12.3982i	−0.629869	+	0.457626i
$735$	45.7239	−	9.64064i	1.68655	−	0.355600i
$736$	−1.30556	−	0.948546i	−0.0481236	−	0.0349639i
$737$	−0.141632	+	0.174901i	−0.00521709	+	0.00644257i
$738$	−21.8353	−	56.8830i	−0.803770	−	2.09389i
$739$	−7.21113	−	0.757921i	−0.265266	−	0.0278806i	−0.0290382	−	0.999578i	$-0.509244\pi$
$739$	−7.21113	−	0.757921i	−0.265266	−	0.0278806i	−0.236228	+	0.971698i	$0.575911\pi$
$740$	−4.58191	−	3.16001i	−0.168434	−	0.116164i
$741$	3.43462	+	4.72735i	0.126174	+	0.173664i
$742$	−86.7471	+	12.5770i	−3.18459	+	0.461716i
$743$	3.41793	−	3.41793i	0.125392	−	0.125392i	−0.641626	−	0.767018i	$-0.721740\pi$
$743$	3.41793	−	3.41793i	0.125392	−	0.125392i	0.767018	+	0.641626i	$0.221740\pi$
$744$	48.1619	−	43.3652i	1.76570	−	1.58984i
$745$	1.09348	+	3.71363i	0.0400619	+	0.136057i
$746$	18.4390	−	20.4786i	0.675101	−	0.749776i
$747$	−44.3550	+	28.8045i	−1.62286	+	1.05390i
$748$	−0.369871	−	2.33527i	−0.0135238	−	0.0853860i
$749$	22.3772	+	25.5167i	0.817644	+	0.932360i
$750$	−74.5759	+	45.2025i	−2.72313	+	1.65056i
$751$	−5.61814	+	9.73090i	−0.205009	+	0.355086i	−0.950136	−	0.311837i	$-0.899056\pi$
$751$	−5.61814	+	9.73090i	−0.205009	+	0.355086i	0.745127	+	0.666923i	$0.232389\pi$
$752$	−30.6718	−	37.8766i	−1.11849	−	1.38122i
$753$	0.0847816	+	1.61773i	0.00308961	+	0.0589534i
$754$	20.5774	+	4.37385i	0.749383	+	0.159286i
$755$	−2.86403	+	11.8449i	−0.104233	+	0.431080i
$756$	13.0512	−	110.261i	0.474668	−	4.01017i
$757$	4.30306	+	4.30306i	0.156397	+	0.156397i	0.780968	−	0.624571i	$-0.214726\pi$
$757$	4.30306	+	4.30306i	0.156397	+	0.156397i	−0.624571	+	0.780968i	$0.714726\pi$
$758$	81.0982	+	4.25018i	2.94562	+	0.154373i
$759$	−0.0447533	−	0.0199255i	−0.00162444	−	0.000723248i
$760$	−18.4714	+	8.77364i	−0.670026	+	0.318253i
$761$	−2.87986	−	6.46828i	−0.104395	−	0.234475i	0.853794	−	0.520611i	$-0.174296\pi$
$761$	−2.87986	−	6.46828i	−0.104395	−	0.234475i	−0.958189	+	0.286136i	$0.907629\pi$
$762$	−11.8862	+	75.0466i	−0.430592	+	2.71865i
$763$	−29.7351	+	1.16805i	−1.07648	+	0.0422862i
$764$	72.6844	−	100.041i	2.62963	−	3.61937i
$765$	−57.6845	+	20.3219i	−2.08559	+	0.734741i
$766$	13.8228	−	31.0465i	0.499439	−	1.12176i
$767$	16.5087	+	10.7209i	0.596096	+	0.387109i
$768$	46.5124	−	12.4630i	1.67837	−	0.449719i
$769$	5.23318	−	16.1061i	0.188713	−	0.580800i	−0.811279	−	0.584659i	$-0.801228\pi$
$769$	5.23318	−	16.1061i	0.188713	−	0.580800i	0.999993	+	0.00385911i	$0.00122840\pi$
$770$	−1.17073	−	1.14420i	−0.0421903	−	0.0412342i
$771$	−15.8690	−	48.8398i	−0.571509	−	1.75892i
$772$	1.45723	+	2.24394i	0.0524468	+	0.0807611i
$773$	8.76806	−	7.10023i	0.315365	−	0.255378i	−0.458548	−	0.888670i	$-0.651630\pi$
$773$	8.76806	−	7.10023i	0.315365	−	0.255378i	0.773913	+	0.633292i	$0.218297\pi$
$774$	−83.2250	+	48.0500i	−2.99146	+	1.72712i
$775$	−14.2118	+	3.75867i	−0.510503	+	0.135015i
$776$		−	79.8783i		−	2.86746i
$777$	−4.01509	−	0.689953i	−0.144041	−	0.0247519i
$778$	−18.7909	−	9.57443i	−0.673686	−	0.343260i
$779$	−1.01569	+	4.77847i	−0.0363910	+	0.171206i
$780$	1.41524	−	50.8913i	0.0506736	−	1.82220i
$781$	0.814908	−	0.173214i	0.0291597	−	0.00619809i
$782$	0.484650	+	1.80874i	0.0173311	+	0.0646804i
$783$	−39.4780	+	20.1150i	−1.41083	+	0.718853i
$784$	−57.5276	−	35.2543i	−2.05456	−	1.25908i
$785$	−8.90295	−	14.5813i	−0.317760	−	0.520430i
$786$	58.6488	−	26.1121i	2.09193	−	0.931388i
$787$	−6.24961	+	2.39900i	−0.222775	+	0.0855151i	−0.467195	−	0.884154i	$-0.654736\pi$
$787$	−6.24961	+	2.39900i	−0.222775	+	0.0855151i	0.244421	+	0.969669i	$0.421402\pi$
$788$	16.0249	−	6.15140i	0.570865	−	0.219134i
$789$	−54.9372	+	24.4596i	−1.95582	+	0.870785i
$790$	−35.1491	+	8.37828i	−1.25055	+	0.298086i
$791$	9.85646	−	3.06042i	0.350455	−	0.108816i
$792$	−4.11971	+	2.09910i	−0.146388	+	0.0745882i
$793$	−3.49979	−	13.0614i	−0.124281	−	0.463824i
$794$	−51.9782	+	11.0483i	−1.84464	+	0.392090i
$795$	51.6407	−	67.0740i	1.83151	−	2.37887i
$796$	2.61260	−	12.2913i	0.0926013	−	0.435655i
$797$	−7.70734	−	3.92708i	−0.273008	−	0.139104i	0.312127	−	0.950040i	$-0.398958\pi$
$797$	−7.70734	−	3.92708i	−0.273008	−	0.139104i	−0.585135	+	0.810936i	$0.698958\pi$
$798$	−16.3443	+	19.6516i	−0.578584	+	0.695659i
$799$			23.3907i			0.827502i
$800$	50.9045	+	10.9928i	1.79975	+	0.388654i
$801$	69.6258	−	40.1985i	2.46011	−	1.42034i
$802$	57.1843	−	46.3069i	2.01925	−	1.63515i
$803$	0.788329	+	1.21392i	0.0278195	+	0.0428383i
$804$	−9.46097	−	29.1179i	−0.333663	−	1.02691i
$805$	0.718912	+	0.568647i	0.0253383	+	0.0200422i
$806$	3.75109	−	11.5447i	0.132126	−	0.406643i
$807$	−7.15048	+	1.91597i	−0.251709	+	0.0674452i
$808$	−57.2878	−	37.2031i	−2.01538	−	1.30880i
$809$	4.03448	−	9.06159i	0.141845	−	0.318588i	−0.828628	−	0.559800i	$-0.810878\pi$
$809$	4.03448	−	9.06159i	0.141845	−	0.318588i	0.970473	+	0.241211i	$0.0775447\pi$
$810$	29.1796	+	38.1556i	1.02527	+	1.34065i
$811$	−6.48171	+	8.92131i	−0.227604	+	0.313270i	−0.907511	−	0.420029i	$-0.862020\pi$
$811$	−6.48171	+	8.92131i	−0.227604	+	0.313270i	0.679907	+	0.733298i	$0.262020\pi$
$812$	2.55369	+	65.0095i	0.0896170	+	2.28139i
$813$	−3.85150	+	24.3174i	−0.135078	+	0.852849i
$814$	0.0580487	+	0.130380i	0.00203461	+	0.00456980i
$815$	5.93422	+	45.6469i	0.207867	+	1.59894i
$816$	121.603	+	54.1411i	4.25695	+	1.89532i
$817$	7.69451	+	0.403252i	0.269197	+	0.0141080i
$818$	7.14040	+	7.14040i	0.249658	+	0.249658i
$819$	−9.75827	−	22.7135i	−0.340982	−	0.793674i
$820$	32.4102	−	27.5902i	1.13181	−	0.963490i
$821$	5.85056	+	1.24357i	0.204186	+	0.0434011i	0.308869	−	0.951105i	$-0.400050\pi$
$821$	5.85056	+	1.24357i	0.204186	+	0.0434011i	−0.104683	+	0.994506i	$0.533383\pi$
$822$	5.37936	+	102.644i	0.187627	+	3.58013i
$823$	−25.4391	−	31.4147i	−0.886752	−	1.09505i	−0.994895	−	0.100912i	$-0.967824\pi$
$823$	−25.4391	−	31.4147i	−0.886752	−	1.09505i	0.108144	−	0.994135i	$-0.465509\pi$
$824$	−24.6511	+	42.6969i	−0.858761	+	1.48742i
$825$	1.58091	+	0.00512814i	0.0550402	+	0.000178539i
$826$	−27.6781	+	81.5348i	−0.963044	+	2.83696i
$827$	−2.34114	−	14.7814i	−0.0814094	−	0.513999i	−0.994371	−	0.105954i	$-0.966211\pi$
$827$	−2.34114	−	14.7814i	−0.0814094	−	0.513999i	0.912962	−	0.408045i	$-0.133789\pi$
$828$	3.70789	−	2.40793i	0.128858	−	0.0836813i
$829$	−8.38379	+	9.31115i	−0.291181	+	0.323389i	−0.870931	−	0.491405i	$-0.836484\pi$
$829$	−8.38379	+	9.31115i	−0.291181	+	0.323389i	0.579750	+	0.814794i	$0.303150\pi$
$830$	−41.4056	−	31.8785i	−1.43721	−	1.10652i
$831$	−28.4846	+	25.6477i	−0.988121	+	0.889708i
$832$	−8.86689	+	8.86689i	−0.307404	+	0.307404i
$833$	10.8085	+	30.5238i	0.374492	+	1.05759i
$834$	−20.1010	−	27.6666i	−0.696040	−	0.958016i
$835$	5.19285	−	17.4269i	0.179706	−	0.603083i
$836$	0.629601	+	0.0661737i	0.0217752	+	0.00228867i
$837$	9.16205	+	23.8680i	0.316687	+	0.824998i
$838$	−11.3936	+	14.0699i	−0.393585	+	0.486037i
$839$	−28.6107	−	20.7869i	−0.987750	−	0.717643i	−0.0283231	−	0.999599i	$-0.509017\pi$
$839$	−28.6107	−	20.7869i	−0.987750	−	0.717643i	−0.959427	+	0.281956i	$0.909017\pi$
$840$	127.239	−	28.5733i	4.39017	−	0.985873i
$841$	−2.45765	+	1.78558i	−0.0847464	+	0.0615719i
$842$	3.12255	−	59.5818i	0.107610	−	2.05333i
$843$	21.1787	−	79.0401i	0.729434	−	2.72228i
$844$	3.66073	+	17.2224i	0.126007	+	0.592818i
$845$	11.1725	+	20.6571i	0.384347	+	0.710625i
$846$	74.2898	−	24.1382i	2.55414	−	0.829889i
$847$	−7.15633	−	28.1791i	−0.245894	−	0.968245i
$848$	−120.719	+	19.1200i	−4.14551	+	0.656584i
$849$	41.1553	+	23.7610i	1.41244	+	0.815475i
$850$	−37.8768	−	47.0854i	−1.29916	−	1.61501i
$851$	−0.0399564	−	0.0692065i	−0.00136969	−	0.00237237i
$852$	−40.6159	+	105.808i	−1.39148	+	3.62493i
$853$	12.7236	−	24.9715i	0.435648	−	0.855007i	−0.563927	−	0.825825i	$-0.690710\pi$
$853$	12.7236	−	24.9715i	0.435648	−	0.855007i	0.999574	−	0.0291816i	$-0.00929012\pi$
$854$	51.6078	−	28.9012i	1.76598	−	0.988978i
$855$	−1.25834	−	16.3272i	−0.0430342	−	0.558378i
$856$	63.3757	+	70.3859i	2.16614	+	2.40574i
$857$	25.2424	+	6.76369i	0.862265	+	0.231043i	0.662740	−	0.748850i	$-0.269394\pi$
$857$	25.2424	+	6.76369i	0.862265	+	0.231043i	0.199525	+	0.979893i	$0.436060\pi$
$858$	−0.710988	+	1.09483i	−0.0242727	+	0.0373767i
$859$	−2.62848	−	25.0083i	−0.0896824	−	0.853271i	−0.943204	−	0.332214i	$-0.892204\pi$
$859$	−2.62848	−	25.0083i	−0.0896824	−	0.853271i	0.853522	−	0.521057i	$-0.174462\pi$
$860$	−50.9766	−	43.6813i	−1.73829	−	1.48952i
$861$	13.0431	−	28.2921i	0.444509	−	0.964193i
$862$	14.2851	+	2.26254i	0.486553	+	0.0770625i
$863$	24.3167	+	19.6913i	0.827751	+	0.670300i	0.946528	−	0.322621i	$-0.104564\pi$
$863$	24.3167	+	19.6913i	0.827751	+	0.670300i	−0.118777	+	0.992921i	$0.537897\pi$
$864$	9.46721	−	90.0745i	0.322081	−	3.06440i
$865$	−11.5410	−	24.2976i	−0.392406	−	0.826142i
$866$	77.6675	−	8.16318i	2.63925	−	0.277396i
$867$	−5.96150	−	11.7001i	−0.202463	−	0.397356i
$868$	37.4602	+	2.45558i	1.27148	+	0.0833479i
$869$	0.622995	+	0.202423i	0.0211337	+	0.00686674i
$870$	−64.3633	−	61.2772i	−2.18212	−	2.07749i
$871$	−2.49551	−	2.24697i	−0.0845572	−	0.0761356i
$872$	−82.9325	+	4.34631i	−2.80845	+	0.147184i
$873$	59.7176	+	22.9235i	2.02114	+	0.775841i
$874$	−0.501379			−0.0169594
$875$	−28.6344	−	7.42096i	−0.968020	−	0.250874i
$876$	−196.907			−6.65288
$877$	−12.8751	−	4.94227i	−0.434760	−	0.166889i	0.131138	−	0.991364i	$-0.458137\pi$
$877$	−12.8751	−	4.94227i	−0.434760	−	0.166889i	−0.565898	+	0.824476i	$0.691470\pi$
$878$	19.2473	−	1.00871i	0.649564	−	0.0340422i
$879$	51.0191	+	45.9378i	1.72083	+	1.54944i
$880$	−1.65321	−	1.57394i	−0.0557298	−	0.0530577i
$881$	−3.33473	−	1.08352i	−0.112350	−	0.0365047i	0.252302	−	0.967648i	$-0.418812\pi$
$881$	−3.33473	−	1.08352i	−0.112350	−	0.0365047i	−0.364652	+	0.931144i	$0.618812\pi$
$882$	85.7911	−	65.8276i	2.88874	−	2.21653i
$883$	−16.0761	−	31.5512i	−0.541005	−	1.06178i	−0.986077	−	0.166288i	$-0.946822\pi$
$883$	−16.0761	−	31.5512i	−0.541005	−	1.06178i	0.445072	−	0.895495i	$-0.353178\pi$
$884$	35.0855	−	3.68763i	1.18005	−	0.124029i
$885$	−35.6769	−	75.1114i	−1.19927	−	2.52484i
$886$	2.46850	−	23.4862i	0.0829310	−	0.789036i
$887$	−0.334381	−	0.270776i	−0.0112274	−	0.00909178i	0.623690	−	0.781672i	$-0.285633\pi$
$887$	−0.334381	−	0.270776i	−0.0112274	−	0.00909178i	−0.634918	+	0.772580i	$0.718966\pi$
$888$	−11.2292	−	1.77854i	−0.376829	−	0.0596838i
$889$	−21.0477	+	14.8748i	−0.705917	+	0.498884i
$890$	60.3205	+	51.6880i	2.02195	+	1.73259i
$891$	−0.0910228	−	0.866025i	−0.00304938	−	0.0290129i
$892$	2.08471	−	3.21017i	0.0698011	−	0.107484i
$893$	−6.04950	−	1.62096i	−0.202439	−	0.0542433i
$894$	9.03585	+	10.0353i	0.302204	+	0.335632i
$895$	2.83406	+	36.7726i	0.0947322	+	1.22917i
$896$	0.225507	+	0.134165i	0.00753366	+	0.00448214i
$897$	0.331847	−	0.651286i	0.0110800	−	0.0217458i
$898$	−1.84472	+	4.80567i	−0.0615592	+	0.160367i
$899$	−7.49033	−	12.9736i	−0.249816	−	0.432695i
$900$	−78.0943	+	119.405i	−2.60314	+	3.98017i
$901$	50.7997	+	29.3292i	1.69238	+	0.977097i
$902$	−1.07795	+	0.170730i	−0.0358917	+	0.00568469i
$903$	−47.2917	−	13.3381i	−1.57377	−	0.443863i
$904$	27.3924	−	8.90032i	0.911057	−	0.296020i
$905$	19.5585	+	36.1620i	0.650145	+	1.20206i
$906$	8.83798	+	41.5794i	0.293622	+	1.38138i
$907$	3.29185	−	12.2853i	0.109304	−	0.407928i	−0.889494	−	0.456947i	$-0.848943\pi$
$907$	3.29185	−	12.2853i	0.109304	−	0.407928i	0.998798	+	0.0490192i	$0.0156095\pi$
$908$	1.99732	−	38.1111i	0.0662833	−	1.26476i
$909$	44.2538	−	32.1523i	1.46781	−	1.06642i
$910$	17.9634	−	16.5510i	0.595481	−	0.548660i
$911$	5.78586	+	4.20367i	0.191694	+	0.139274i	0.679493	−	0.733682i	$-0.262200\pi$
$911$	5.78586	+	4.20367i	0.191694	+	0.139274i	−0.487799	+	0.872956i	$0.662200\pi$
$912$	−22.4295	+	27.6981i	−0.742714	+	0.917176i
$913$	0.339490	+	0.884402i	0.0112355	+	0.0292694i
$914$	−5.29230	−	0.556244i	−0.175054	−	0.0183989i
$915$	−16.3124	+	54.7436i	−0.539272	+	1.80977i
$916$	59.5532	+	81.9680i	1.96769	+	2.70830i
$917$	20.2261	+	8.06961i	0.667926	+	0.266482i
$918$	−74.3130	+	74.3130i	−2.45270	+	2.45270i
$919$	−38.5665	+	34.7254i	−1.27219	+	1.14549i	−0.290117	+	0.956991i	$0.593694\pi$
$919$	−38.5665	+	34.7254i	−1.27219	+	1.14549i	−0.982074	+	0.188495i	$0.939639\pi$
$920$	2.02689	+	1.56052i	0.0668247	+	0.0514488i
$921$	−20.0051	+	22.2179i	−0.659189	+	0.732104i
$922$	59.0708	−	38.3610i	1.94539	−	1.26335i
$923$	1.94461	+	12.2778i	0.0640076	+	0.404128i
$924$	−3.82293	−	1.29775i	−0.125765	−	0.0426927i
$925$	2.08143	+	1.52259i	0.0684369	+	0.0500623i
$926$	−8.31699	+	14.4055i	−0.273313	+	0.473393i
$927$	−24.8462	−	30.6825i	−0.816057	−	1.00775i
$928$	2.77750	+	52.9979i	0.0911760	+	1.73974i
$929$	−18.5149	−	3.93545i	−0.607453	−	0.129118i	−0.106092	−	0.994356i	$-0.533834\pi$
$929$	−18.5149	−	3.93545i	−0.607453	−	0.129118i	−0.501361	+	0.865238i	$0.667167\pi$
$930$	−39.0464	+	33.2394i	−1.28038	+	1.08996i
$931$	−8.64337	+	0.680104i	−0.283275	+	0.0222895i
$932$	59.1597	+	59.1597i	1.93784	+	1.93784i
$933$	20.3143	+	1.06462i	0.665059	+	0.0348543i
$934$	57.2216	+	25.4767i	1.87235	+	0.833623i
$935$	0.141229	+	1.08635i	0.00461868	+	0.0355276i
$936$	−28.0605	−	63.0249i	−0.917186	−	2.06003i
$937$	3.85562	−	24.3434i	0.125958	−	0.795266i	−0.841132	−	0.540830i	$-0.818110\pi$
$937$	3.85562	−	24.3434i	0.125958	−	0.795266i	0.967090	−	0.254436i	$-0.0818897\pi$
$938$	6.83949	−	12.9995i	0.223317	−	0.424448i
$939$	16.2683	−	22.3914i	0.530895	−	0.730714i
$940$	33.1478	+	43.3445i	1.08116	+	1.41374i
$941$	16.9821	−	38.1424i	0.553600	−	1.24341i	−0.392566	−	0.919724i	$-0.628413\pi$
$941$	16.9821	−	38.1424i	0.553600	−	1.24341i	0.946166	−	0.323682i	$-0.104921\pi$
$942$	−49.9801	−	32.4574i	−1.62844	−	1.05752i
$943$	0.590281	−	0.158165i	0.0192222	−	0.00515057i
$944$	−37.1015	+	114.187i	−1.20755	+	3.71646i
$945$	−7.46487	+	50.8999i	−0.242832	+	1.65577i
$946$	0.531927	+	1.63710i	0.0172944	+	0.0532268i
$947$	18.5704	+	28.5959i	0.603456	+	0.929240i	0.999937	+	0.0111977i	$0.00356441\pi$
$947$	18.5704	+	28.5959i	0.603456	+	0.929240i	−0.396482	+	0.918043i	$0.629769\pi$
$948$	−69.2539	+	56.0807i	−2.24926	+	1.82142i
$949$	−18.7036	+	10.7985i	−0.607145	+	0.350535i
$950$	14.8025	−	6.53304i	0.480256	−	0.211960i
$951$		−	53.5562i		−	1.73668i
$952$	31.2765	+	84.7809i	1.01368	+	2.74777i
$953$	3.18846	+	1.62460i	0.103284	+	0.0526261i	0.504870	−	0.863196i	$-0.331541\pi$
$953$	3.18846	+	1.62460i	0.103284	+	0.0526261i	−0.401585	+	0.915822i	$0.631541\pi$
$954$	40.7277	−	191.609i	1.31861	−	6.20356i
$955$	−34.9526	+	45.3984i	−1.13104	+	1.46906i
$956$	−48.4136	+	10.2906i	−1.56581	+	0.332822i
$957$	0.416971	+	1.55616i	0.0134788	+	0.0503034i
$958$	−3.90164	+	1.98798i	−0.126056	+	0.0642289i
$959$	−23.6666	+	25.6020i	−0.764234	+	0.826730i
$960$	51.5284	−	12.2825i	1.66307	−	0.396417i
$961$	20.4231	−	9.09296i	0.658810	−	0.293321i
$962$	−1.98805	+	0.763140i	−0.0640972	+	0.0246046i
$963$	−70.8086	+	27.1809i	−2.28178	+	0.875891i
$964$	−121.653	+	54.1635i	−3.91819	+	1.74449i
$965$	−0.646020	−	1.05806i	−0.0207961	−	0.0340600i
$966$	3.11854	+	0.705680i	0.100337	+	0.0227049i
$967$	−19.1875	+	9.77652i	−0.617028	+	0.314392i	−0.734421	−	0.678694i	$-0.762546\pi$
$967$	−19.1875	+	9.77652i	−0.617028	+	0.314392i	0.117393	+	0.993086i	$0.462546\pi$
$968$	−20.9996	−	78.3715i	−0.674952	−	2.51896i
$969$	16.7312	−	3.55632i	0.537483	−	0.114245i
$970$	−1.75692	+	63.1780i	−0.0564112	+	2.02852i
$971$	11.3496	−	53.3956i	0.364225	−	1.71355i	−0.289813	−	0.957083i	$-0.593593\pi$
$971$	11.3496	−	53.3956i	0.364225	−	1.71355i	0.654038	−	0.756462i	$-0.273074\pi$
$972$	−6.62503	−	3.37562i	−0.212498	−	0.108273i
$973$	1.96455	−	11.4324i	0.0629805	−	0.366507i
$974$		−	80.5628i		−	2.58140i
$975$	−1.31094	+	23.5523i	−0.0419838	+	0.754277i
$976$	71.4272	−	41.2385i	2.28633	−	1.32001i
$977$	10.0596	−	8.14609i	0.321835	−	0.260616i	−0.454764	−	0.890612i	$-0.650277\pi$
$977$	10.0596	−	8.14609i	0.321835	−	0.260616i	0.776599	+	0.629995i	$0.216943\pi$
$978$	87.4508	+	134.662i	2.79637	+	4.30603i
$979$	−0.445009	−	1.36960i	−0.0142225	−	0.0437725i
$980$	63.2854	+	41.2456i	2.02158	+	1.31754i
$981$	20.5506	−	63.2483i	0.656131	−	2.01936i
$982$	15.9967	−	4.28629i	0.510474	−	0.136781i
$983$	6.54156	+	4.24814i	0.208643	+	0.135495i	0.644731	−	0.764410i	$-0.276970\pi$
$983$	6.54156	+	4.24814i	0.208643	+	0.135495i	−0.436087	+	0.899904i	$0.643636\pi$
$984$	35.3624	−	79.4253i	1.12731	−	2.53199i
$985$	−7.50124	+	2.64264i	−0.239009	+	0.0842017i
$986$	36.1964	−	49.8201i	1.15273	−	1.58660i
$987$	35.3460	+	18.5968i	1.12508	+	0.591943i
$988$	−1.47768	+	9.32968i	−0.0470112	+	0.296817i
$989$	−0.392031	−	0.880516i	−0.0124659	−	0.0279988i
$990$	3.30457	−	1.56962i	0.105026	−	0.0498859i
$991$	20.9600	+	9.33198i	0.665815	+	0.296440i	0.711676	−	0.702508i	$-0.247936\pi$
$991$	20.9600	+	9.33198i	0.665815	+	0.296440i	−0.0458609	+	0.998948i	$0.514603\pi$
$992$	30.5808	+	1.60267i	0.970940	+	0.0508848i
$993$	−44.9754	−	44.9754i	−1.42725	−	1.42725i
$994$	−49.9600	+	21.4640i	−1.58464	+	0.680797i
$995$	−1.36835	+	5.65913i	−0.0433795	+	0.179406i
$996$	−126.057	−	26.7941i	−3.99425	−	0.849005i
$997$	0.593593	+	11.3264i	0.0187993	+	0.358712i	0.991791	+	0.127871i	$0.0408143\pi$
$997$	0.593593	+	11.3264i	0.0187993	+	0.358712i	−0.972992	+	0.230841i	$0.925852\pi$
$998$	68.8637	+	85.0396i	2.17984	+	2.69188i
$999$	2.24251	−	3.88414i	0.0709499	−	0.122889i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.12.1	✓	288
5.2	odd	4		875.2.bb.a.418.18		288
5.3	odd	4		875.2.bb.b.418.1		288
5.4	even	2		875.2.bb.c.82.18		288
7.3	odd	6	inner	175.2.x.a.87.18	yes	288
25.2	odd	20		875.2.bb.c.593.1		288
25.11	even	5		875.2.bb.b.782.1		288
25.14	even	10		875.2.bb.a.782.18		288
25.23	odd	20	inner	175.2.x.a.173.18	yes	288
35.3	even	12		875.2.bb.b.668.1		288
35.17	even	12		875.2.bb.a.668.18		288
35.24	odd	6		875.2.bb.c.332.1		288
175.52	even	60		875.2.bb.c.843.18		288
175.73	even	60	inner	175.2.x.a.73.1	yes	288
175.136	odd	30		875.2.bb.b.157.1		288
175.164	odd	30		875.2.bb.a.157.18		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.12.1	✓	288	1.1	even	1	trivial
175.2.x.a.73.1	yes	288	175.73	even	60	inner
175.2.x.a.87.18	yes	288	7.3	odd	6	inner
175.2.x.a.173.18	yes	288	25.23	odd	20	inner
875.2.bb.a.157.18		288	175.164	odd	30
875.2.bb.a.418.18		288	5.2	odd	4
875.2.bb.a.668.18		288	35.17	even	12
875.2.bb.a.782.18		288	25.14	even	10
875.2.bb.b.157.1		288	175.136	odd	30
875.2.bb.b.418.1		288	5.3	odd	4
875.2.bb.b.668.1		288	35.3	even	12
875.2.bb.b.782.1		288	25.11	even	5
875.2.bb.c.82.18		288	5.4	even	2
875.2.bb.c.332.1		288	35.24	odd	6
875.2.bb.c.593.1		288	25.2	odd	20
875.2.bb.c.843.18		288	175.52	even	60

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.43914 - 0.936298i) q^{2} +(2.98133 - 0.156245i) q^{3} +(3.58646 + 3.22926i) q^{4} +(-1.61949 - 1.54184i) q^{5} +(-7.41816 - 2.41031i) q^{6} +(-1.17017 - 2.37291i) q^{7} +(-3.35206 - 6.57879i) q^{8} +(5.88033 - 0.618047i) q^{9} +(2.50654 + 5.27708i) q^{10} +(0.0110705 - 0.105329i) q^{11} +(11.1969 + 9.06711i) q^{12} +(1.56081 + 0.247208i) q^{13} +(0.632446 + 6.88349i) q^{14} +(-5.06913 - 4.34368i) q^{15} +(1.00752 + 9.58587i) q^{16} +(2.51942 - 3.87956i) q^{17} +(-14.9216 - 3.99823i) q^{18} +(0.828774 + 0.920447i) q^{19} +(-0.829232 - 10.7595i) q^{20} +(-3.85940 - 6.89159i) q^{21} +(-0.125622 + 0.246547i) q^{22} +(0.0555245 - 0.144646i) q^{23} +(-11.0215 - 19.0898i) q^{24} +(0.245482 + 4.99397i) q^{25} +(-3.57557 - 2.06436i) q^{26} +(8.58862 - 1.36030i) q^{27} +(3.46600 - 12.2891i) q^{28} +(-4.84593 + 1.57454i) q^{29} +(8.29732 + 15.3411i) q^{30} +(0.611278 + 2.87584i) q^{31} +(2.69575 - 10.0607i) q^{32} +(0.0165478 - 0.315750i) q^{33} +(-9.77764 + 7.10387i) q^{34} +(-1.76357 + 5.64711i) q^{35} +(23.0854 + 16.7725i) q^{36} +(0.324588 - 0.400833i) q^{37} +(-1.15968 - 3.02108i) q^{38} +(4.69190 + 0.493139i) q^{39} +(-4.71479 + 15.8226i) q^{40} +(2.31834 + 3.19093i) q^{41} +(2.96104 + 20.4231i) q^{42} +(4.39882 - 4.39882i) q^{43} +(0.379839 - 0.342008i) q^{44} +(-10.4760 - 8.06558i) q^{45} +(-0.270864 + 0.300825i) q^{46} +(-4.24074 + 2.75397i) q^{47} +(4.50147 + 28.4212i) q^{48} +(-4.26142 + 5.55340i) q^{49} +(4.07708 - 12.4108i) q^{50} +(6.90505 - 11.9599i) q^{51} +(4.79947 + 5.92685i) q^{52} +(0.663649 + 12.6632i) q^{53} +(-22.2225 - 4.72354i) q^{54} +(-0.180329 + 0.153510i) q^{55} +(-11.6884 + 15.6524i) q^{56} +(2.61466 + 2.61466i) q^{57} +(13.2941 + 0.696716i) q^{58} +(11.3795 + 5.06647i) q^{59} +(-4.15332 - 31.9479i) q^{60} +(-3.48040 - 7.81711i) q^{61} +(1.20165 - 7.58691i) q^{62} +(-8.34753 - 13.2303i) q^{63} +(-4.66418 + 6.41969i) q^{64} +(-2.14656 - 2.80686i) q^{65} +(-0.335998 + 0.754665i) q^{66} +(-1.78216 - 1.15735i) q^{67} +(21.5639 - 5.77803i) q^{68} +(0.142937 - 0.439913i) q^{69} +(9.58897 - 12.1228i) q^{70} +(2.43082 + 7.48129i) q^{71} +(-23.7772 - 36.6137i) q^{72} +(-10.6211 + 8.60076i) q^{73} +(-1.16701 + 0.673776i) q^{74} +(1.51214 + 14.8503i) q^{75} +5.97747i q^{76} +(-0.262891 + 0.0969831i) q^{77} +(-10.9825 - 5.59585i) q^{78} +(-1.28595 + 6.04991i) q^{79} +(13.1482 - 17.0776i) q^{80} +(8.04241 - 1.70947i) q^{81} +(-2.66710 - 9.95377i) q^{82} +(-7.96975 + 4.06079i) q^{83} +(8.41316 - 37.1794i) q^{84} +(-10.0618 + 2.39838i) q^{85} +(-14.8479 + 6.61073i) q^{86} +(-14.2013 + 5.45136i) q^{87} +(-0.730047 + 0.280239i) q^{88} +(12.4217 - 5.53052i) q^{89} +(18.0007 + 29.4818i) q^{90} +(-1.23980 - 3.99294i) q^{91} +(0.666237 - 0.339465i) q^{92} +(2.27175 + 8.47830i) q^{93} +(12.9223 - 2.74672i) q^{94} +(0.0769888 - 2.76849i) q^{95} +(6.46499 - 30.4154i) q^{96} +(9.63928 + 4.91146i) q^{97} +(15.5938 - 9.55556i) q^{98} -0.626212i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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